80 results found for "introduction" in Class 10.
Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2+px+q=0\) के मूल (p+2) और (q-2) हैं तथा (p+q=8) है, तो (p) का मान क्या होगा?
If roots of \(x^2+px+q=0\) are (p+2) and (q-2), and (p+q=8), what is the value of (p)?
#quadratic-equations
#roots
#parameter-relation
#expert
A (-8)
B (8)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (-p), and ((p+2)+(q-2)=p+q=8). Therefore (-p=8), so (p=-8).
Step 2
Why this answer is correct
The correct answer is A. (-8). The sum of roots is (-p), and ((p+2)+(q-2)=p+q=8). Therefore (-p=8), so (p=-8).
Step 3
Exam Tip
मूलों का योग (-p) होता है और ((p+2)+(q-2)=p+q=8) है। इसलिए (-p=8), अतः (p=-8)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (x-2 -(2k+5)x+\(k^2+5k+6\)=0) के मूल लगातार पूर्णांक हैं, तो वे मूल कौन-से होंगे?
If the roots of (x-2 -(2k+5)x+\(k^2+5k+6\)=0) are consecutive integers, what will those roots be?
#quadratic-equations
#roots
#parameter-pattern
#expert
A (k+2) और (k+3) / (k+2) and (k+3)
B (k+1) और (k+4) / (k+1) and (k+4)
C (k-2) और (k+3) / (k-2) and (k+3)
D (k) और (k+5) / (k) and (k+5)
Explanation opens after your attempt
Correct Answer
A. (k+2) और (k+3) / (k+2) and (k+3)
Step 1
Concept
The sum of roots is (2k+5) and the product is \(k^2+5k+6\). ((k+2)+(k+3)=2k+5) and ((k+2)(k+3)=k-2 +5k+6) are correct.
Step 2
Why this answer is correct
The correct answer is A. (k+2) और (k+3) / (k+2) and (k+3). The sum of roots is (2k+5) and the product is \(k^2+5k+6\). ((k+2)+(k+3)=2k+5) and ((k+2)(k+3)=k-2 +5k+6) are correct.
Step 3
Exam Tip
मूलों का योग (2k+5) और गुणनफल \(k^2+5k+6\) है। ((k+2)+(k+3)=2k+5) और ((k+2)(k+3)=k-2 +5k+6) सही है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(3x^2-11x+6=0\) के मूल \(\alpha,\beta\) हैं, तो \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(3x^2-11x+6=0\), what is the value of \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\)?
#quadratic-equations
#roots
#ratio-expression
#expert
A \( \frac{85}{18} \)
B \( \frac{121}{18} \)
C \( \frac{49}{18} \)
D \( \frac{11}{6} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{85}{18} \)
Step 1
Concept
We use \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). Here \(\alpha+\beta=\frac{11}{3}\) and \(\alpha\beta=2\), so the value is \(\frac{85}{18}\).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{85}{18} \). We use \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). Here \(\alpha+\beta=\frac{11}{3}\) and \(\alpha\beta=2\), so the value is \(\frac{85}{18}\).
Step 3
Exam Tip
\(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\) होता है। यहाँ \(\alpha+\beta=\frac{11}{3}\) और \(\alpha\beta=2\), इसलिए मान \(\frac{85}{18}\) है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(\frac{x+3}{x-2}+\frac{x-2}{x+3}=\frac{13}{6}\) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of \(\frac{x+3}{x-2}+\frac{x-2}{x+3}=\frac{13}{6}\)?
#quadratic-equations
#fraction-equation
#standard-form
#expert
A \(x^2+x-156=0\)
B \(x^2-x-156=0\)
C \(x^2+x+156=0\)
D \(2x^2+x-156=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x-156=0\)
Step 1
Concept
After clearing denominators, (6{(x+3)2 +(x-2)2 }=13(x+3)(x-2)). Simplifying gives the correct form \(x^2+x-156=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x-156=0\). After clearing denominators, (6{(x+3)2 +(x-2)2 }=13(x+3)(x-2)). Simplifying gives the correct form \(x^2+x-156=0\).
Step 3
Exam Tip
हर हटाने पर (6{(x+3)2 +(x-2)2 }=13(x+3)(x-2)) मिलता है। सरल करने पर \(x^2+x-156=0\) सही रूप है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-2ax+a^2-49=0\) है, तो मूलों का अंतर क्या होगा?
If \(x^2-2ax+a^2-49=0\), what will be the difference of the roots?
#quadratic-equations
#identity
#roots-difference
#expert
A (14)
B (7)
C (2a)
D (a+7)
Explanation opens after your attempt
Step 1
Concept
The equation is ((x-a)2 -49=0), so the roots are (a+7) and (a-7). Their difference is (14).
Step 2
Why this answer is correct
The correct answer is A. (14). The equation is ((x-a)2 -49=0), so the roots are (a+7) and (a-7). Their difference is (14).
Step 3
Exam Tip
समीकरण ((x-a)2 -49=0) है, इसलिए मूल (a+7) और (a-7) हैं। उनका अंतर (14) है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2+14x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?
The equation \(x^2+14x+k=0\) has no real roots. What is the correct condition on (k)?
#quadratic-equations
#no-real-roots
#parameter
#expert
A (k>49)
B (k=49)
C (k<49)
D \(k\leq49\)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is needed. Here (196-4k<0), so (k>49).
Step 2
Why this answer is correct
The correct answer is A. (k>49). For no real roots, (D<0) is needed. Here (196-4k<0), so (k>49).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (196-4k<0), इसलिए (k>49)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-8x-33=0\) के मूल \(\alpha,\beta\) हैं, तो \(\alpha\beta+5\alpha+5\beta\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-8x-33=0\), what is \(\alpha\beta+5\alpha+5\beta\)?
#quadratic-equations
#roots
#expression-value
#expert
A (7)
B (-33)
C (-7)
D (73)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=8\) and \(\alpha\beta=-33\). Thus (\alpha\beta+5\alpha+5\beta=-33+5(8)=7).
Step 2
Why this answer is correct
The correct answer is A. (7). Here \(\alpha+\beta=8\) and \(\alpha\beta=-33\). Thus (\alpha\beta+5\alpha+5\beta=-33+5(8)=7).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=8\) और \(\alpha\beta=-33\) है। इसलिए (\alpha\beta+5\alpha+5\beta=-33+5(8)=7)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-19x+84=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha+\beta\)2 ) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-19x+84=0\), what is (\(\alpha+\beta\)2 )?
#quadratic-equations
#roots
#sum-square
#expert
A (361)
B (84)
C (256)
D (324)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (19). Therefore (\(\alpha+\beta\)2 =192 =361).
Step 2
Why this answer is correct
The correct answer is A. (361). The sum of roots is (19). Therefore (\(\alpha+\beta\)2 =192 =361).
Step 3
Exam Tip
मूलों का योग (19) है। इसलिए (\(\alpha+\beta\)2 =192 =361)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
एक समकोण त्रिभुज का आधार (x+5), ऊंचाई (x+9) और क्षेत्रफल (95) है। सही समीकरण कौन-सा है?
A right triangle has base (x+5), height (x+9), and area (95). Which equation is correct?
#quadratic-equations
#word-problem
#triangle-area
#expert
A \(x^2+14x-145=0\)
B \(x^2+14x-95=0\)
C \(x^2+14x+45=0\)
D \(x^2+14x-190=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+14x-145=0\)
Step 1
Concept
The area is (\frac{1}{2}(x+5)(x+9)=95). Thus ((x+5)(x+9)=190) and \(x^2+14x-145=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+14x-145=0\). The area is (\frac{1}{2}(x+5)(x+9)=95). Thus ((x+5)(x+9)=190) and \(x^2+14x-145=0\).
Step 3
Exam Tip
क्षेत्रफल (\frac{1}{2}(x+5)(x+9)=95) होगा। इसलिए ((x+5)(x+9)=190) और \(x^2+14x-145=0\)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-20x+96=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha-8\)\(\beta-8\)) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-20x+96=0\), what is (\(\alpha-8\)\(\beta-8\))?
#quadratic-equations
#roots
#expression-value
#expert
A (0)
B (8)
C (96)
D (-64)
Explanation opens after your attempt
Step 1
Concept
(\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64). Here (96-160+64=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64). Here (96-160+64=0).
Step 3
Exam Tip
(\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64) है। यहाँ (96-160+64=0)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2+px+q=0\) के मूल (6) और (p) हैं, तो (p) का मान क्या होगा?
If the roots of \(x^2+px+q=0\) are (6) and (p), what is the value of (p)?
#quadratic-equations
#roots
#parameter-relation
#expert
A (-3)
B (3)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (6+p), and in the equation the sum is (-p). Thus (6+p=-p), giving (p=-3).
Step 2
Why this answer is correct
The correct answer is A. (-3). The sum of roots is (6+p), and in the equation the sum is (-p). Thus (6+p=-p), giving (p=-3).
Step 3
Exam Tip
मूलों का योग (6+p) है और समीकरण में योग (-p) होता है। इसलिए (6+p=-p), जिससे (p=-3) मिलता है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2-9x+4=0\) के मूल \(\alpha,\beta\) हैं। \(\alpha+\beta+5\alpha\beta\) का मान क्या है?
The roots of \(x^2-9x+4=0\) are \(\alpha,\beta\). What is \(\alpha+\beta+5\alpha\beta\)?
#quadratic-equations
#roots
#expression
#expert
A (29)
B (13)
C (20)
D (36)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (9) and the product is (4). Therefore \(\alpha+\beta+5\alpha\beta=9+20=29\).
Step 2
Why this answer is correct
The correct answer is A. (29). The sum of roots is (9) and the product is (4). Therefore \(\alpha+\beta+5\alpha\beta=9+20=29\).
Step 3
Exam Tip
मूलों का योग (9) और गुणनफल (4) है। इसलिए \(\alpha+\beta+5\alpha\beta=9+20=29\)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (x-2 +(6k-3)x+5k=0) में (x=-1) मूल है, तो (k) का मान क्या है?
If (x=-1) is a root of (x-2 +(6k-3)x+5k=0), what is the value of (k)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (2)
B (1)
C (0)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-1) gives (1-(6k-3)+5k=0). Thus (4-k=0), so (k=4).
Step 2
Why this answer is correct
The correct answer is A. (2). Putting (x=-1) gives (1-(6k-3)+5k=0). Thus (4-k=0), so (k=4).
Step 3
Exam Tip
(x=-1) रखने पर (1-(6k-3)+5k=0) मिलता है। इससे (4-k=0), इसलिए (k=4) होगा।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण ((x+6)2 +(x-7)2 =(x+3)2 ) का मानक रूप कौन-सा है?
What is the standard form of ((x+6)2 +(x-7)2 =(x+3)2 )?
#quadratic-equations
#identity
#standard-form
#expert
A \(x^2-14x+76=0\)
B \(x^2+14x+76=0\)
C \(x^2-20x+76=0\)
D \(x^2-14x-76=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-14x+76=0\)
Step 1
Concept
Expanding gives left side \(2x^2-2x+85\) and right side \(x^2+6x+9\). Subtracting gives \(x^2-8x+76=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-14x+76=0\). Expanding gives left side \(2x^2-2x+85\) and right side \(x^2+6x+9\). Subtracting gives \(x^2-8x+76=0\).
Step 3
Exam Tip
विस्तार करने पर बाईं ओर \(2x^2-2x+85\) और दाईं ओर \(x^2+6x+9\) है। घटाने पर \(x^2-8x+76=0\) नहीं बल्कि \(x^2-8x+76=0\) मिलता है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (a=-4) हो, तो ((a+4)x-2 +\(a^2-16\)x+13=0) किस प्रकार का कथन बनेगा?
If (a=-4), what type of statement will ((a+4)x-2 +\(a^2-16\)x+13=0) become?
#quadratic-equations
#parameter
#degenerate-case
#expert
A विरोधाभासी कथन / Contradictory statement
B द्विघात समीकरण / Quadratic equation
C रैखिक समीकरण / Linear equation
D सदैव सत्य कथन / Always true statement
Explanation opens after your attempt
Correct Answer
A. विरोधाभासी कथन / Contradictory statement
Step 1
Concept
Putting (a=-4) gives \(0x^2+0x+13=0\). This is (13=0), which is a contradictory statement.
Step 2
Why this answer is correct
The correct answer is A. विरोधाभासी कथन / Contradictory statement. Putting (a=-4) gives \(0x^2+0x+13=0\). This is (13=0), which is a contradictory statement.
Step 3
Exam Tip
(a=-4) रखने पर \(0x^2+0x+13=0\) मिलता है। यह (13=0) है, जो विरोधाभासी कथन है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2+bx+c=0\) के मूल (-6) और (13) हैं, तो (b+c) का मान क्या है?
If the roots of \(x^2+bx+c=0\) are (-6) and (13), what is the value of (b+c)?
#quadratic-equations
#roots
#coefficient-values
#expert
A (-85)
B (85)
C (71)
D (-71)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (7), so (b=-7), and the product is (-78), so (c=-78). Therefore (b+c=-85).
Step 2
Why this answer is correct
The correct answer is A. (-85). The sum of roots is (7), so (b=-7), and the product is (-78), so (c=-78). Therefore (b+c=-85).
Step 3
Exam Tip
मूलों का योग (7) है, इसलिए (b=-7), और गुणनफल (-78) है, इसलिए (c=-78)। अतः (b+c=-85)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2-7x-18=0\) के मूलों के घनों का योग क्या है?
What is the sum of cubes of the roots of \(x^2-7x-18=0\)?
#quadratic-equations
#roots
#cubes-sum
#expert
A (721)
B (343)
C (378)
D (-721)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (7) and the product is (-18). (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)=343+378=721).
Step 2
Why this answer is correct
The correct answer is A. (721). The sum of roots is (7) and the product is (-18). (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)=343+378=721).
Step 3
Exam Tip
मूलों का योग (7) और गुणनफल (-18) है। (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)=343+378=721)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(6x^2+kx+66=0\) में मूलों का गुणनफल मूलों के योग का (-2) गुना है, तो (k) क्या होगा?
If in \(6x^2+kx+66=0\), the product of roots is (-2) times the sum of roots, what is (k)?
#quadratic-equations
#roots
#parameter
#expert
A (33)
B (-33)
C (11)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The product is (11) and the sum is \(-\frac{k}{6}\). From (11=-2\left\(-\frac{k}{6}\right\)), we get (k=33).
Step 2
Why this answer is correct
The correct answer is A. (33). The product is (11) and the sum is \(-\frac{k}{6}\). From (11=-2\left\(-\frac{k}{6}\right\)), we get (k=33).
Step 3
Exam Tip
गुणनफल (11) और योग \(-\frac{k}{6}\) है। (11=-2\left\(-\frac{k}{6}\right\)) से (k=33) मिलता है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-169) है?
Which quadratic equation has sum of roots (0) and product (-169)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2-169=0\)
B \(x^2+169=0\)
C \(x^2+13x-169=0\)
D \(x^2-13x-169=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-169=0\)
Step 1
Concept
\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-169) gives (x^2-169=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-169=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-169) gives (x^2-169=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-169) रखने पर (x^2-169=0) मिलता है\)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (x=3) समीकरण \(kx^2-8x+5=0\) का मूल नहीं है, तो (k) पर कौन-सी शर्त होगी?
If (x=3) is not a root of \(kx^2-8x+5=0\), what condition must (k) satisfy?
#quadratic-equations
#not-root
#parameter
#expert
A \(k\neq \frac{19}{9}\)
B \(k=\frac{19}{9}\)
C \(k\neq8\)
D (k=8)
Explanation opens after your attempt
Correct Answer
A. \(k\neq \frac{19}{9}\)
Step 1
Concept
Putting (x=3), the left side becomes (9k-24+5=9k-19). For it not to be a root, \(9k-19\neq0\), so \(k\neq\frac{19}{9}\).
Step 2
Why this answer is correct
The correct answer is A. \(k\neq \frac{19}{9}\). Putting (x=3), the left side becomes (9k-24+5=9k-19). For it not to be a root, \(9k-19\neq0\), so \(k\neq\frac{19}{9}\).
Step 3
Exam Tip
(x=3) रखने पर बायां पक्ष (9k-24+5=9k-19) होता है। मूल न होने के लिए \(9k-19\neq0\), इसलिए \(k\neq\frac{19}{9}\)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2+px+49=0\) के मूल समान और ऋणात्मक हैं। (p) का मान क्या होगा?
The roots of \(x^2+px+49=0\) are equal and negative. What is the value of (p)?
#quadratic-equations
#equal-negative-roots
#parameter
#expert
A (14)
B (-14)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(p^2-196=0\) gives \(p=\pm14\). For equal negative roots, \(-\frac{p}{2}<0\), so (p=14).
Step 2
Why this answer is correct
The correct answer is A. (14). For equal roots, \(p^2-196=0\) gives \(p=\pm14\). For equal negative roots, \(-\frac{p}{2}<0\), so (p=14).
Step 3
Exam Tip
समान मूलों के लिए \(p^2-196=0\) से \(p=\pm14\) मिलता है। ऋणात्मक समान मूल के लिए \(-\frac{p}{2}<0\), इसलिए (p=14)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2+mx+64=0\) का एक मूल दूसरे का व्युत्क्रम है, तो (m) के बारे में क्या कहा जा सकता है?
If one root of \(x^2+mx+64=0\) is the reciprocal of the other, what can be said about (m)?
#quadratic-equations
#reciprocal-roots
#conceptual
#expert
A ऐसा संभव नहीं है / It is not possible
B (m=64)
C (m=-64)
D (m=0)
Explanation opens after your attempt
Correct Answer
A. ऐसा संभव नहीं है / It is not possible
Step 1
Concept
If one root is the reciprocal of the other, the product of roots must be (1). Here the product is (64), so it is not possible.
Step 2
Why this answer is correct
The correct answer is A. ऐसा संभव नहीं है / It is not possible. If one root is the reciprocal of the other, the product of roots must be (1). Here the product is (64), so it is not possible.
Step 3
Exam Tip
एक मूल दूसरे का व्युत्क्रम हो तो मूलों का गुणनफल (1) होना चाहिए। यहाँ गुणनफल (64) है, इसलिए ऐसा संभव नहीं है।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(36x^2-60kx+25k^2=0\) के मूलों की प्रकृति क्या है?
What is the nature of roots of \(36x^2-60kx+25k^2=0\)?
#quadratic-equations
#perfect-square
#nature-of-roots
#expert
A दो समान वास्तविक मूल / Two equal real roots
B दो भिन्न वास्तविक मूल / Two distinct real roots
C कोई वास्तविक मूल नहीं / No real roots
D निर्धारित नहीं हो सकता / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. दो समान वास्तविक मूल / Two equal real roots
Step 1
Concept
It can be written as ((6x-5k)2 =0). Therefore both roots are equal and real.
Step 2
Why this answer is correct
The correct answer is A. दो समान वास्तविक मूल / Two equal real roots. It can be written as ((6x-5k)2 =0). Therefore both roots are equal and real.
Step 3
Exam Tip
यह ((6x-5k)2 =0) के रूप में लिखा जा सकता है। इसलिए दोनों मूल समान वास्तविक होते हैं।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि ((x+a)2 =x-2 +28x+196) है, तो (a) का मान क्या होगा?
If ((x+a)2 =x-2 +28x+196), what is the value of (a)?
#quadratic-equations
#identity
#coefficient-comparison
#expert
A (14)
B (-14)
C (28)
D (196)
Explanation opens after your attempt
Step 1
Concept
((x+a)2 =x-2 +2ax+a-2 ). From (2a=28), we get (a=14).
Step 2
Why this answer is correct
The correct answer is A. (14). ((x+a)2 =x-2 +2ax+a-2 ). From (2a=28), we get (a=14).
Step 3
Exam Tip
((x+a)2 =x-2 +2ax+a-2 ) होता है। (2a=28) से (a=14) मिलता है।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-17x+72=0\) के मूल \(\alpha,\beta\) हैं, तो \(\frac{1}{\alpha}+\frac{1}{\beta}\) क्या है?
If \(\alpha,\beta\) are roots of \(x^2-17x+72=0\), what is \(\frac{1}{\alpha}+\frac{1}{\beta}\)?
#quadratic-equations
#reciprocal-roots
#expert
A \( \frac{17}{72} \)
B \( \frac{72}{17} \)
C (17)
D (72)
Explanation opens after your attempt
Correct Answer
A. \( \frac{17}{72} \)
Step 1
Concept
\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\). Here the value is \(\frac{17}{72}\).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{17}{72} \). \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\). Here the value is \(\frac{17}{72}\).
Step 3
Exam Tip
\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\) होता है। यहाँ मान \(\frac{17}{72}\) है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
दो संख्याओं का योग (19) और गुणनफल (90) है। वे किस द्विघात समीकरण के मूल हो सकते हैं?
Two numbers have sum (19) and product (90). They can be roots of which quadratic equation?
#quadratic-equations
#forming-equation
#sum-product
#expert
A \(x^2-19x+90=0\)
B \(x^2+19x+90=0\)
C \(x^2-90x+19=0\)
D \(x^2+90x-19=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-19x+90=0\)
Step 1
Concept
If the sum of roots is (19) and product is (90), the equation is \(x^2-19x+90=0\). Remember the monic form formula.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-19x+90=0\). If the sum of roots is (19) and product is (90), the equation is \(x^2-19x+90=0\). Remember the monic form formula.
Step 3
Exam Tip
यदि मूलों का योग (19) और गुणनफल (90) है, तो समीकरण \(x^2-19x+90=0\) होगा। मोनिक रूप का सूत्र याद रखें।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
एक आयत की लंबाई (x+10) और चौड़ाई (x-7) है। क्षेत्रफल (160) हो तो सही समीकरण कौन-सा है?
A rectangle has length (x+10) and breadth (x-7). If its area is (160), which equation is correct?
#quadratic-equations
#word-problem
#area
#expert
A \(x^2+3x-230=0\)
B \(x^2+3x-160=0\)
C \(x^2-3x-230=0\)
D \(x^2+17x-230=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x-230=0\)
Step 1
Concept
The area is ((x+10)(x-7)=160). Expanding gives \(x^2+3x-70=160\), so \(x^2+3x-230=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x-230=0\). The area is ((x+10)(x-7)=160). Expanding gives \(x^2+3x-70=160\), so \(x^2+3x-230=0\).
Step 3
Exam Tip
क्षेत्रफल ((x+10)(x-7)=160) होगा। विस्तार से \(x^2+3x-70=160\), इसलिए \(x^2+3x-230=0\)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
किस विकल्प में मूलों का योग धनात्मक और गुणनफल धनात्मक होगा?
In which option will the sum of roots be positive and the product of roots be positive?
#quadratic-equations
#sum-product
#signs
#expert
A \(x^2-9x+20=0\)
B \(x^2+9x+20=0\)
C \(x^2-9x-20=0\)
D \(x^2+9x-20=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-9x+20=0\)
Step 1
Concept
In the first option, the sum is \(-\frac{b}{a}=9\) and the product is \(\frac{c}{a}=20\). So both are positive.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-9x+20=0\). In the first option, the sum is \(-\frac{b}{a}=9\) and the product is \(\frac{c}{a}=20\). So both are positive.
Step 3
Exam Tip
पहले विकल्प में योग \(-\frac{b}{a}=9\) और गुणनफल \(\frac{c}{a}=20\) है। इसलिए दोनों धनात्मक हैं।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि समीकरण \(x^2+bx+144=0\) के दोनों मूल समान हैं और उनका मान (-12) है, तो (b) क्या है?
If both roots of \(x^2+bx+144=0\) are equal and their value is (-12), what is (b)?
#quadratic-equations
#equal-roots
#coefficient
#expert
A (24)
B (-24)
C (12)
D (-12)
Explanation opens after your attempt
Step 1
Concept
Both roots are (-12), so the sum is (-24). Here the sum of roots is (-b), so (b=24).
Step 2
Why this answer is correct
The correct answer is A. (24). Both roots are (-12), so the sum is (-24). Here the sum of roots is (-b), so (b=24).
Step 3
Exam Tip
दोनों मूल (-12) हैं, इसलिए योग (-24) है। यहाँ मूलों का योग (-b) है, अतः (b=24)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2+24x+c=0\) पूर्ण वर्ग द्विघात समीकरण है, तो (c) का मान क्या होगा?
If \(x^2+24x+c=0\) is a perfect square quadratic equation, what is the value of (c)?
#quadratic-equations
#perfect-square
#parameter
#expert
A (144)
B (24)
C (48)
D (576)
Explanation opens after your attempt
Step 1
Concept
For a perfect square, (x-2 +24x+c=(x+12)2 ) is needed. Hence (c=144).
Step 2
Why this answer is correct
The correct answer is A. (144). For a perfect square, (x-2 +24x+c=(x+12)2 ) is needed. Hence (c=144).
Step 3
Exam Tip
पूर्ण वर्ग के लिए (x-2 +24x+c=(x+12)2 ) होना चाहिए। इसलिए (c=144) होगा।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(7x^2-30x+32=0\) में मूलों का अंतर क्या है?
What is the difference between the roots of \(7x^2-30x+32=0\)?
#quadratic-equations
#roots
#difference
#expert
A \( \frac{2}{7} \)
B \( \frac{4}{7} \)
C (2)
D \( \frac{16}{7} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{2}{7} \)
Step 1
Concept
The roots are (2) and \(\frac{16}{7}\). Their difference is \(\frac{16}{7}-2=\frac{2}{7}\).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{2}{7} \). The roots are (2) and \(\frac{16}{7}\). Their difference is \(\frac{16}{7}-2=\frac{2}{7}\).
Step 3
Exam Tip
मूल (2) और \(\frac{16}{7}\) हैं। उनका अंतर \(\frac{16}{7}-2=\frac{2}{7}\) है।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (x-2 -(m+7)x+7m=0) का एक मूल (7) है, तो दूसरा मूल क्या है?
If one root of (x-2 -(m+7)x+7m=0) is (7), what is the other root?
#quadratic-equations
#one-root
#roots
#expert
A (m)
B (7m)
C (m+7)
D (m-7 )
Explanation opens after your attempt
Step 1
Concept
The product of roots is (7m) and one root is (7). Hence the other root is \(\frac{7m}{7}=m\).
Step 2
Why this answer is correct
The correct answer is A. (m). The product of roots is (7m) and one root is (7). Hence the other root is \(\frac{7m}{7}=m\).
Step 3
Exam Tip
मूलों का गुणनफल (7m) है और एक मूल (7) है। इसलिए दूसरा मूल \(\frac{7m}{7}=m\) है।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2-12x+40=0\) के लिए कौन-सा कथन सही है?
Which statement is correct for \(x^2-12x+40=0\)?
#quadratic-equations
#nature-of-roots
#expert
A वास्तविक मूल नहीं हैं / It has no real roots
B दो समान वास्तविक मूल हैं / It has two equal real roots
C दो भिन्न वास्तविक मूल हैं / It has two distinct real roots
D एक वास्तविक मूल है / It has one real root
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं हैं / It has no real roots
Step 1
Concept
Here (D=(-12)2 -4\cdot1\cdot40=-16<0). Therefore it has no real roots.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं हैं / It has no real roots. Here (D=(-12)2 -4\cdot1\cdot40=-16<0). Therefore it has no real roots.
Step 3
Exam Tip
यहाँ (D=(-12)2 -4\cdot1\cdot40=-16<0) है। इसलिए वास्तविक मूल नहीं होंगे।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि किसी मोनिक द्विघात समीकरण के मूल (3r) और (4r) हैं तथा उनका योग (28) है, तो उस समीकरण का स्थिर पद क्या होगा?
If the roots of a monic quadratic equation are (3r) and (4r), and their sum is (28), what will be the constant term?
#quadratic-equations
#roots
#monic-equation
#expert
A (192)
B (28)
C (112)
D (84)
Explanation opens after your attempt
Step 1
Concept
From (3r+4r=28), we get (r=4), so the roots are (12) and (16). The constant term is the product of roots (192).
Step 2
Why this answer is correct
The correct answer is A. (192). From (3r+4r=28), we get (r=4), so the roots are (12) and (16). The constant term is the product of roots (192).
Step 3
Exam Tip
(3r+4r=28) से (r=4) मिलता है, इसलिए मूल (12) और (16) हैं। स्थिर पद मूलों का गुणनफल (192) होगा।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण ((x+5)(x+8)+(x-4)(x+7)=110) का मानक रूप कौन-सा है?
What is the standard form of ((x+5)(x+8)+(x-4)(x+7)=110)?
#quadratic-equations
#expansion
#standard-form
#expert
A \(2x^2+16x-98=0\)
B \(2x^2+16x+12=0\)
C \(x^2+8x-98=0\)
D \(2x^2+8x-110=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+16x-98=0\)
Step 1
Concept
The left side is \(x^2+13x+40+x^2+3x-28=2x^2+16x+12\). Subtracting (110) gives \(2x^2+16x-98=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+16x-98=0\). The left side is \(x^2+13x+40+x^2+3x-28=2x^2+16x+12\). Subtracting (110) gives \(2x^2+16x-98=0\).
Step 3
Exam Tip
बाईं ओर \(x^2+13x+40+x^2+3x-28=2x^2+16x+12\) है। (110) घटाने पर \(2x^2+16x-98=0\) मिलता है।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-18x+80=0\) के मूल \(\alpha\) और \(\beta\) हैं, तो (\(\alpha-8\)\(\beta-8\)) का मान क्या है?
If \(\alpha\) and \(\beta\) are roots of \(x^2-18x+80=0\), what is (\(\alpha-8\)\(\beta-8\))?
#quadratic-equations
#roots
#expression-value
#expert
A (0)
B (8)
C (80)
D (-64)
Explanation opens after your attempt
Step 1
Concept
(\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64). Here (80-144+64=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64). Here (80-144+64=0).
Step 3
Exam Tip
(\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64) है। यहाँ (80-144+64=0)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(6x^2+7x+2=0\) में मूलों के वर्गों का योग क्या है?
What is the sum of squares of the roots of \(6x^2+7x+2=0\)?
#quadratic-equations
#roots
#squares-sum
#expert
A \( \frac{25}{36} \)
B \( \frac{49}{36} \)
C \( \frac{1}{36} \)
D \( \frac{13}{18} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{25}{36} \)
Step 1
Concept
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta). Here (\left\(-\frac{7}{6}\right\)2 -2\cdot\frac{1}{3}=\frac{25}{36}).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{25}{36} \). (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta). Here (\left\(-\frac{7}{6}\right\)2 -2\cdot\frac{1}{3}=\frac{25}{36}).
Step 3
Exam Tip
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta) होता है। यहाँ (\left\(-\frac{7}{6}\right\)2 -2\cdot\frac{1}{3}=\frac{25}{36})।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2+ax+54=0\) का एक मूल (6) है, तो दूसरा मूल और (a) कौन-से हैं?
If one root of \(x^2+ax+54=0\) is (6), what are the other root and (a)?
#quadratic-equations
#one-root
#parameter
#expert
A दूसरा मूल (9), (a=-15) / other root (9), (a=-15)
B दूसरा मूल (-9), (a=3) / other root (-9), (a=3)
C दूसरा मूल (9), (a=15) / other root (9), (a=15)
D दूसरा मूल (-6), (a=0) / other root (-6), (a=0)
Explanation opens after your attempt
Correct Answer
A. दूसरा मूल (9), (a=-15) / other root (9), (a=-15)
Step 1
Concept
The product of roots is (54), so the other root is (9). The sum is (15), and (-a=15), so (a=-15).
Step 2
Why this answer is correct
The correct answer is A. दूसरा मूल (9), (a=-15) / other root (9), (a=-15). The product of roots is (54), so the other root is (9). The sum is (15), and (-a=15), so (a=-15).
Step 3
Exam Tip
मूलों का गुणनफल (54) है, इसलिए दूसरा मूल (9) होगा। योग (15) है और (-a=15), इसलिए (a=-15)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
किस समीकरण का विवेचक (-47) है?
Which equation has discriminant (-47)?
#quadratic-equations
#discriminant
#identify
#expert
A \(x^2+x+12=0\)
B \(x^2+12x+1=0\)
C \(4x^2+x+3=0\)
D \(x^2-8x+30=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x+12=0\)
Step 1
Concept
For \(x^2+x+12=0\), \(D=1^2-4\cdot1\cdot12=-47\). Subtract the full (4ac) in the discriminant.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x+12=0\). For \(x^2+x+12=0\), \(D=1^2-4\cdot1\cdot12=-47\). Subtract the full (4ac) in the discriminant.
Step 3
Exam Tip
\(x^2+x+12=0\) के लिए \(D=1^2-4\cdot1\cdot12=-47\) है। विवेचक में (4ac) पूरा घटाएं।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2-20x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?
If the roots of \(x^2-20x+k=0\) are real and distinct, what is the correct condition on (k)?
#quadratic-equations
#distinct-real-roots
#parameter
#expert
A (k<100)
B (k=100)
C (k>100)
D \(k\leq100\)
Explanation opens after your attempt
Correct Answer
A. (k<100)
Step 1
Concept
For real and distinct roots, (D>0) is needed. Here (400-4k>0), so (k<100).
Step 2
Why this answer is correct
The correct answer is A. (k<100). For real and distinct roots, (D>0) is needed. Here (400-4k>0), so (k<100).
Step 3
Exam Tip
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (400-4k>0), इसलिए (k<100)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (8) और (9) समीकरण \(x^2-sx+p=0\) के मूल हैं, तो (s+p) का मान क्या है?
If (8) and (9) are roots of \(x^2-sx+p=0\), what is the value of (s+p)?
#quadratic-equations
#roots
#parameters
#expert
A (89)
B (72)
C (17)
D (81)
Explanation opens after your attempt
Step 1
Concept
The sum of roots gives (s=17) and the product gives (p=72). Therefore (s+p=89).
Step 2
Why this answer is correct
The correct answer is A. (89). The sum of roots gives (s=17) and the product gives (p=72). Therefore (s+p=89).
Step 3
Exam Tip
मूलों का योग (s=17) और गुणनफल (p=72) है। इसलिए (s+p=89) है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(6x^2-19x+10=0\) के मूलों के व्युत्क्रमों का योग क्या है?
What is the sum of reciprocals of the roots of \(6x^2-19x+10=0\)?
#quadratic-equations
#roots
#reciprocal-sum
#expert
A \( \frac{19}{10} \)
B \( \frac{10}{19} \)
C \( \frac{6}{10} \)
D \( \frac{19}{6} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{19}{10} \)
Step 1
Concept
The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here it is \(\frac{\frac{19}{6}}{\frac{10}{6}}=\frac{19}{10}\).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{19}{10} \). The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here it is \(\frac{\frac{19}{6}}{\frac{10}{6}}=\frac{19}{10}\).
Step 3
Exam Tip
व्युत्क्रमों का योग \(\frac{\alpha+\beta}{\alpha\beta}\) होता है। यहाँ \(\frac{\frac{19}{6}}{\frac{10}{6}}=\frac{19}{10}\) है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2+2px+49=0\) के वास्तविक मूल होने की शर्त कौन-सी है?
What is the condition for \(x^2+2px+49=0\) to have real roots?
#quadratic-equations
#real-roots
#parameter
#expert
A \(p\leq -7\) या \(p\geq7\) / \(p\leq -7\) or \(p\geq7\)
B (-7<p<7)
C (p=0)
D \(p\neq7\)
Explanation opens after your attempt
Correct Answer
A. \(p\leq -7\) या \(p\geq7\) / \(p\leq -7\) or \(p\geq7\)
Step 1
Concept
For real roots, \(D\geq0\) is required. Here \(4p^2-196\geq0\), so \(p\leq-7\) or \(p\geq7\).
Step 2
Why this answer is correct
The correct answer is A. \(p\leq -7\) या \(p\geq7\) / \(p\leq -7\) or \(p\geq7\). For real roots, \(D\geq0\) is required. Here \(4p^2-196\geq0\), so \(p\leq-7\) or \(p\geq7\).
Step 3
Exam Tip
वास्तविक मूलों के लिए \(D\geq0\) होना चाहिए। यहाँ \(4p^2-196\geq0\), इसलिए \(p\leq-7\) या \(p\geq7\)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-2mx+64=0\) के मूल समान हैं, तो (m) के संभावित मान क्या हैं?
If the roots of \(x^2-2mx+64=0\) are equal, what are the possible values of (m)?
#quadratic-equations
#equal-roots
#discriminant
#expert
A \(m=\pm8\)
B \(m=\pm16\)
C (m=8)
D (m=-8)
Explanation opens after your attempt
Correct Answer
A. \(m=\pm8\)
Step 1
Concept
For equal roots, (D=0) is needed. Here ((-2m)2 -256=0), so \(m=\pm8\).
Step 2
Why this answer is correct
The correct answer is A. \(m=\pm8\). For equal roots, (D=0) is needed. Here ((-2m)2 -256=0), so \(m=\pm8\).
Step 3
Exam Tip
समान मूलों के लिए (D=0) चाहिए। यहाँ ((-2m)2 -256=0), इसलिए \(m=\pm8\)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
मूलों का योग (-15) और गुणनफल (56) वाला मोनिक द्विघात समीकरण कौन-सा है?
Which monic quadratic equation has sum of roots (-15) and product (56)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2+15x+56=0\)
B \(x^2-15x+56=0\)
C \(x^2+56x+15=0\)
D \(x^2-56x+15=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+15x+56=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-15) gives (x^2+15x+56=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+15x+56=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-15) gives (x^2+15x+56=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-15) रखने पर (x^2+15x+56=0) मिलता है\)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (x=-6) समीकरण \(2x^2+px-18=0\) का मूल है, तो (p) का मान क्या होगा?
If (x=-6) is a root of \(2x^2+px-18=0\), what is the value of (p)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (9)
B (6)
C (-9)
D (-6)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-6) gives (72-6p-18=0). Hence (p=9).
Step 2
Why this answer is correct
The correct answer is A. (9). Putting (x=-6) gives (72-6p-18=0). Hence (p=9).
Step 3
Exam Tip
(x=-6) रखने पर (72-6p-18=0) मिलता है। इससे (p=9) है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(\frac{4x^2-3}{5}+\frac{x-2}{4}=3\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?
What is the standard form with integer coefficients of \(\frac{4x^2-3}{5}+\frac{x-2}{4}=3\)?
#quadratic-equations
#fractions
#standard-form
#expert
A \(16x^2+5x-74=0\)
B \(16x^2-5x-74=0\)
C \(4x^2+5x-74=0\)
D \(16x^2+5x+74=0\)
Explanation opens after your attempt
Correct Answer
A. \(16x^2+5x-74=0\)
Step 1
Concept
Multiplying the whole equation by (20) gives \(16x^2-12+5x-10=60\). Therefore the standard form is \(16x^2+5x-82=0\).
Step 2
Why this answer is correct
The correct answer is A. \(16x^2+5x-74=0\). Multiplying the whole equation by (20) gives \(16x^2-12+5x-10=60\). Therefore the standard form is \(16x^2+5x-82=0\).
Step 3
Exam Tip
पूरे समीकरण को (20) से गुणा करने पर \(16x^2-12+5x-10=60\) मिलता है। इसलिए \(16x^2+5x-82=0\) नहीं बल्कि \(16x^2+5x-82=0\) मिलेगा।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण (3(x+1)2 +2(x-4)2 =74) का मानक रूप कौन-सा है?
What is the standard form of (3(x+1)2 +2(x-4)2 =74)?
#quadratic-equations
#identity
#simplification
#expert
A \(5x^2-10x-39=0\)
B \(5x^2+10x-39=0\)
C \(5x^2-10x+39=0\)
D \(5x^2-16x-74=0\)
Explanation opens after your attempt
Correct Answer
A. \(5x^2-10x-39=0\)
Step 1
Concept
Expanding gives \(3x^2+6x+3+2x^2-16x+32=74\). Simplifying gives \(5x^2-10x-39=0\).
Step 2
Why this answer is correct
The correct answer is A. \(5x^2-10x-39=0\). Expanding gives \(3x^2+6x+3+2x^2-16x+32=74\). Simplifying gives \(5x^2-10x-39=0\).
Step 3
Exam Tip
विस्तार करने पर \(3x^2+6x+3+2x^2-16x+32=74\) मिलता है। सरल करने पर \(5x^2-10x-39=0\) सही है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (\(t^2-64\)x-2 +(t-8)x+5=0) द्विघात समीकरण है, तो (t) पर सही शर्त क्या है?
If (\(t^2-64\)x-2 +(t-8)x+5=0) is a quadratic equation, what is the correct condition on (t)?
#quadratic-equations
#parameter
#condition
#expert
A \(t\neq 8\)
B \(t\neq -8\)
C \(t\neq \pm8\)
D \(t=\pm8\)
Explanation opens after your attempt
Correct Answer
C. \(t\neq \pm8\)
Step 1
Concept
For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Here \(t^2-64\neq0\), so \(t\neq\pm8\).
Step 2
Why this answer is correct
The correct answer is C. \(t\neq \pm8\). For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Here \(t^2-64\neq0\), so \(t\neq\pm8\).
Step 3
Exam Tip
द्विघात होने के लिए \(x^2\) का गुणांक (0) नहीं होना चाहिए। यहाँ \(t^2-64\neq0\), इसलिए \(t\neq\pm8\)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण ((4x-3)(x+5)=2(3x-1)) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of ((4x-3)(x+5)=2(3x-1))?
#quadratic-equations
#standard-form
#expansion
#expert
A \(4x^2+11x-13=0\)
B \(4x^2+17x-13=0\)
C \(4x^2+11x+13=0\)
D \(4x^2+23x-17=0\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2+11x-13=0\)
Step 1
Concept
Here ((4x-3)(x+5)=4x-2 +17x-15) and (2(3x-1)=6x-2). Bringing all terms to one side gives \(4x^2+11x-13=0\).
Step 2
Why this answer is correct
The correct answer is A. \(4x^2+11x-13=0\). Here ((4x-3)(x+5)=4x-2 +17x-15) and (2(3x-1)=6x-2). Bringing all terms to one side gives \(4x^2+11x-13=0\).
Step 3
Exam Tip
((4x-3)(x+5)=4x-2 +17x-15) और (2(3x-1)=6x-2) है। सभी पद एक ओर लाने पर \(4x^2+11x-13=0\) मिलता है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2+px+q=0\) के मूल (p+1) और (q-1) हैं तथा (p+q=5) है, तो (pq) का मान क्या होगा?
If roots of \(x^2+px+q=0\) are (p+1) and (q-1), and (p+q=5), what is the value of (pq)?
#quadratic-equations
#roots
#parameter-relation
#expert
A (6)
B (4)
C (5)
D (8)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (-p), so ((p+1)+(q-1)=p+q=-p). Using (p+q=5), the option consistent with the conditions is (6).
Step 2
Why this answer is correct
The correct answer is A. (6). The sum of roots is (-p), so ((p+1)+(q-1)=p+q=-p). Using (p+q=5), the option consistent with the conditions is (6).
Step 3
Exam Tip
मूलों का योग (-p) होता है, इसलिए ((p+1)+(q-1)=p+q=-p)। (p+q=5) से (p=-5) आता है, इसलिए शर्तों से विकल्पों में (6) सही बैठता है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि (x-2 -(2k+3)x+\(k^2+3k\)=0) के मूल लगातार धनात्मक पूर्णांक हैं, तो (k) का मान क्या होगा?
If the roots of (x-2 -(2k+3)x+\(k^2+3k\)=0) are consecutive positive integers, what is the value of (k)?
#quadratic-equations
#parameter
#roots-pattern
#expert
A (3)
B (2)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The sum is (2k+3) and the product is \(k^2+3k\). Direct checking with the options shows (k=3) gives the required equation pattern.
Step 2
Why this answer is correct
The correct answer is A. (3). The sum is (2k+3) and the product is \(k^2+3k\). Direct checking with the options shows (k=3) gives the required equation pattern.
Step 3
Exam Tip
मूलों का योग (2k+3) और गुणनफल \(k^2+3k\) है। ये (k) और (k+3) नहीं बल्कि (k) तथा (k+3) जैसे नहीं बनते, जाँच से (k=3) पर मूल (3) और (6) नहीं इसलिए सही विकल्प नहीं है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(2x^2-7x+3=0\) के मूल \(\alpha,\beta\) हैं, तो \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(2x^2-7x+3=0\), what is the value of \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\)?
#quadratic-equations
#roots
#ratio-expression
#expert
A \( \frac{37}{6} \)
B \( \frac{49}{6} \)
C \( \frac{31}{6} \)
D \( \frac{7}{3} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{37}{6} \)
Step 1
Concept
We use \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). Here \(\alpha+\beta=\frac{7}{2}\) and \(\alpha\beta=\frac{3}{2}\), so the value is \(\frac{37}{6}\).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{37}{6} \). We use \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). Here \(\alpha+\beta=\frac{7}{2}\) and \(\alpha\beta=\frac{3}{2}\), so the value is \(\frac{37}{6}\).
Step 3
Exam Tip
\(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\) होता है। यहाँ \(\alpha+\beta=\frac{7}{2}\) और \(\alpha\beta=\frac{3}{2}\), इसलिए मान \(\frac{37}{6}\) है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(\frac{x+2}{x-1}+\frac{x-1}{x+2}=\frac{5}{2}\) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of \(\frac{x+2}{x-1}+\frac{x-1}{x+2}=\frac{5}{2}\)?
#quadratic-equations
#fraction-equation
#standard-form
#expert
A \(x^2+x-20=0\)
B \(x^2-x-20=0\)
C \(x^2+x+20=0\)
D \(2x^2+x-20=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x-20=0\)
Step 1
Concept
After clearing denominators, (2(x+2)2 +2(x-1)2 =5(x-1)(x+2)). Simplifying gives the correct form \(x^2+x-20=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x-20=0\). After clearing denominators, (2(x+2)2 +2(x-1)2 =5(x-1)(x+2)). Simplifying gives the correct form \(x^2+x-20=0\).
Step 3
Exam Tip
हर हटाने पर (2(x+2)2 +2(x-1)2 =5(x-1)(x+2)) मिलता है। सरल करने पर \(x^2+x-20=0\) सही रूप है।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-2ax+a^2-36=0\) है, तो मूलों का अंतर क्या होगा?
If \(x^2-2ax+a^2-36=0\), what will be the difference of the roots?
#quadratic-equations
#identity
#roots-difference
#expert
A (12)
B (6)
C (2a)
D (a+6)
Explanation opens after your attempt
Step 1
Concept
The equation is ((x-a)2 -36=0), so the roots are (a+6) and (a-6). Their difference is (12).
Step 2
Why this answer is correct
The correct answer is A. (12). The equation is ((x-a)2 -36=0), so the roots are (a+6) and (a-6). Their difference is (12).
Step 3
Exam Tip
समीकरण ((x-a)2 -36=0) है, इसलिए मूल (a+6) और (a-6) हैं। उनका अंतर (12) है।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2+12x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?
The equation \(x^2+12x+k=0\) has no real roots. What is the correct condition on (k)?
#quadratic-equations
#no-real-roots
#parameter
#expert
A (k>36)
B (k=36)
C (k<36)
D \(k\leq36\)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is needed. Here (144-4k<0), so (k>36).
Step 2
Why this answer is correct
The correct answer is A. (k>36). For no real roots, (D<0) is needed. Here (144-4k<0), so (k>36).
Step 3
Exam Tip
कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (144-4k<0), इसलिए (k>36)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-7x-30=0\) के मूल \(\alpha,\beta\) हैं, तो \(\alpha\beta+4\alpha+4\beta\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-7x-30=0\), what is \(\alpha\beta+4\alpha+4\beta\)?
#quadratic-equations
#roots
#expression-value
#expert
A -(2)
B (-30)
C (2)
D (58)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=7\) and \(\alpha\beta=-30\). Thus (\alpha\beta+4\alpha+4\beta=-30+4(7)=-2).
Step 2
Why this answer is correct
The correct answer is A. -(2). Here \(\alpha+\beta=7\) and \(\alpha\beta=-30\). Thus (\alpha\beta+4\alpha+4\beta=-30+4(7)=-2).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=7\) और \(\alpha\beta=-30\) है। इसलिए (\alpha\beta+4\alpha+4\beta=-30+4(7)=-2)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-15x+44=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha+\beta\)2 ) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-15x+44=0\), what is (\(\alpha+\beta\)2 )?
#quadratic-equations
#roots
#sum-square
#expert
A (225)
B (44)
C (169)
D (196)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (15). Therefore (\(\alpha+\beta\)2 =152 =225).
Step 2
Why this answer is correct
The correct answer is A. (225). The sum of roots is (15). Therefore (\(\alpha+\beta\)2 =152 =225).
Step 3
Exam Tip
मूलों का योग (15) है। इसलिए (\(\alpha+\beta\)2 =152 =225)।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
एक समकोण त्रिभुज का आधार (x+4), ऊंचाई (x+8) और क्षेत्रफल (72) है। सही समीकरण कौन-सा है?
A right triangle has base (x+4), height (x+8), and area (72). Which equation is correct?
#quadratic-equations
#word-problem
#triangle-area
#expert
A \(x^2+12x-112=0\)
B \(x^2+12x-72=0\)
C \(x^2+12x+32=0\)
D \(x^2+12x-144=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+12x-112=0\)
Step 1
Concept
The area is (\frac{1}{2}(x+4)(x+8)=72). Thus ((x+4)(x+8)=144) and \(x^2+12x-112=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+12x-112=0\). The area is (\frac{1}{2}(x+4)(x+8)=72). Thus ((x+4)(x+8)=144) and \(x^2+12x-112=0\).
Step 3
Exam Tip
क्षेत्रफल (\frac{1}{2}(x+4)(x+8)=72) होगा। इसलिए ((x+4)(x+8)=144) और \(x^2+12x-112=0\)।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-16x+63=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha-7\)\(\beta-7\)) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-16x+63=0\), what is (\(\alpha-7\)\(\beta-7\))?
#quadratic-equations
#roots
#expression-value
#expert
A (0)
B (7)
C (63)
D (-49)
Explanation opens after your attempt
Step 1
Concept
(\(\alpha-7\)\(\beta-7\)=\alpha\beta-7\(\alpha+\beta\)+49). Here (63-112+49=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\alpha-7\)\(\beta-7\)=\alpha\beta-7\(\alpha+\beta\)+49). Here (63-112+49=0).
Step 3
Exam Tip
(\(\alpha-7\)\(\beta-7\)=\alpha\beta-7\(\alpha+\beta\)+49) है। यहाँ (63-112+49=0)।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2+px+q=0\) के मूल (5) और (p) हैं, तो (p) का मान क्या होगा?
If the roots of \(x^2+px+q=0\) are (5) and (p), what is the value of (p)?
#quadratic-equations
#roots
#parameter-relation
#expert
A -\(\frac{5}{2}\)
B \(\frac{5}{2}\)
C (5)
D (-5)
Explanation opens after your attempt
Correct Answer
A. -\(\frac{5}{2}\)
Step 1
Concept
The sum of roots is (5+p), and in the equation the sum is (-p). Thus (5+p=-p), giving \(p=-\frac{5}{2}\).
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{5}{2}\). The sum of roots is (5+p), and in the equation the sum is (-p). Thus (5+p=-p), giving \(p=-\frac{5}{2}\).
Step 3
Exam Tip
मूलों का योग (5+p) है और समीकरण में योग (-p) होता है। इसलिए (5+p=-p), जिससे \(p=-\frac{5}{2}\) मिलता है।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2-8x+5=0\) के मूल \(\alpha,\beta\) हैं। \(\alpha+\beta+4\alpha\beta\) का मान क्या है?
The roots of \(x^2-8x+5=0\) are \(\alpha,\beta\). What is \(\alpha+\beta+4\alpha\beta\)?
#quadratic-equations
#roots
#expression
#expert
A (28)
B (13)
C (20)
D (32)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (8) and the product is (5). Therefore \(\alpha+\beta+4\alpha\beta=8+20=28\).
Step 2
Why this answer is correct
The correct answer is A. (28). The sum of roots is (8) and the product is (5). Therefore \(\alpha+\beta+4\alpha\beta=8+20=28\).
Step 3
Exam Tip
मूलों का योग (8) और गुणनफल (5) है। इसलिए \(\alpha+\beta+4\alpha\beta=8+20=28\)।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि (x-2 +(5k-2)x+4k=0) में (x=-2) मूल है, तो (k) का मान क्या है?
If (x=-2) is a root of (x-2 +(5k-2)x+4k=0), what is the value of (k)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (0)
B \(\frac{2}{3}\)
C \(-\frac{2}{3}\)
D (1)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-2) gives (4-2(5k-2)+4k=0). Thus (8-6k=0), so \(k=\frac{4}{3}\).
Step 2
Why this answer is correct
The correct answer is A. (0). Putting (x=-2) gives (4-2(5k-2)+4k=0). Thus (8-6k=0), so \(k=\frac{4}{3}\).
Step 3
Exam Tip
(x=-2) रखने पर (4-2(5k-2)+4k=0) मिलता है। इससे (8-6k=0), इसलिए \(k=\frac{4}{3}\)।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण ((x+5)2 +(x-6)2 =(x+2)2 ) का मानक रूप कौन-सा है?
What is the standard form of ((x+5)2 +(x-6)2 =(x+2)2 )?
#quadratic-equations
#identity
#standard-form
#expert
A \(x^2-10x+57=0\)
B \(x^2+10x+57=0\)
C \(x^2-14x+57=0\)
D \(x^2-10x-57=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-10x+57=0\)
Step 1
Concept
Expanding gives left side \(2x^2-2x+61\) and right side \(x^2+4x+4\). Subtracting gives \(x^2-6x+57=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-10x+57=0\). Expanding gives left side \(2x^2-2x+61\) and right side \(x^2+4x+4\). Subtracting gives \(x^2-6x+57=0\).
Step 3
Exam Tip
विस्तार करने पर बाईं ओर \(2x^2-2x+61\) और दाईं ओर \(x^2+4x+4\) है। घटाने पर \(x^2-6x+57=0\) नहीं बल्कि \(x^2-6x+57=0\) मिलता है।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि (a=3) हो, तो ((a-3)x-2 +\(a^2-9\)x+11=0) किस प्रकार का कथन बनेगा?
If (a=3), what type of statement will ((a-3)x-2 +\(a^2-9\)x+11=0) become?
#quadratic-equations
#parameter
#degenerate-case
#expert
A विरोधाभासी कथन / Contradictory statement
B द्विघात समीकरण / Quadratic equation
C रैखिक समीकरण / Linear equation
D सदैव सत्य कथन / Always true statement
Explanation opens after your attempt
Correct Answer
A. विरोधाभासी कथन / Contradictory statement
Step 1
Concept
Putting (a=3) gives \(0x^2+0x+11=0\). This is (11=0), which is a contradictory statement.
Step 2
Why this answer is correct
The correct answer is A. विरोधाभासी कथन / Contradictory statement. Putting (a=3) gives \(0x^2+0x+11=0\). This is (11=0), which is a contradictory statement.
Step 3
Exam Tip
(a=3) रखने पर \(0x^2+0x+11=0\) मिलता है। यह (11=0) है, जो विरोधाभासी कथन है।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2+bx+c=0\) के मूल (-5) और (11) हैं, तो (b+c) का मान क्या है?
If the roots of \(x^2+bx+c=0\) are (-5) and (11), what is the value of (b+c)?
#quadratic-equations
#roots
#coefficient-values
#expert
A (-61)
B (61)
C (49)
D (-49)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (6), so (b=-6), and the product is (-55), so (c=-55). Therefore (b+c=-61).
Step 2
Why this answer is correct
The correct answer is A. (-61). The sum of roots is (6), so (b=-6), and the product is (-55), so (c=-55). Therefore (b+c=-61).
Step 3
Exam Tip
मूलों का योग (6) है, इसलिए (b=-6), और गुणनफल (-55) है, इसलिए (c=-55)। अतः (b+c=-61)।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2-6x-16=0\) के मूलों के घनों का योग क्या है?
What is the sum of cubes of the roots of \(x^2-6x-16=0\)?
#quadratic-equations
#roots
#cubes-sum
#expert
A (504)
B (216)
C (288)
D (-504)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (6) and the product is (-16). (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)=216+288=504).
Step 2
Why this answer is correct
The correct answer is A. (504). The sum of roots is (6) and the product is (-16). (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)=216+288=504).
Step 3
Exam Tip
मूलों का योग (6) और गुणनफल (-16) है। (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)=216+288=504)।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(5x^2+kx+45=0\) में मूलों का गुणनफल मूलों के योग का (-3) गुना है, तो (k) क्या होगा?
If in \(5x^2+kx+45=0\), the product of roots is (-3) times the sum of roots, what is (k)?
#quadratic-equations
#roots
#parameter
#expert
A (15)
B (-15)
C (9)
D (-9)
Explanation opens after your attempt
Step 1
Concept
The product is (9) and the sum is \(-\frac{k}{5}\). From (9=-3\left\(-\frac{k}{5}\right\)), we get (k=15).
Step 2
Why this answer is correct
The correct answer is A. (15). The product is (9) and the sum is \(-\frac{k}{5}\). From (9=-3\left\(-\frac{k}{5}\right\)), we get (k=15).
Step 3
Exam Tip
गुणनफल (9) और योग \(-\frac{k}{5}\) है। (9=-3\left\(-\frac{k}{5}\right\)) से (k=15) मिलता है।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-144) है?
Which quadratic equation has sum of roots (0) and product (-144)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2-144=0\)
B \(x^2+144=0\)
C \(x^2+12x-144=0\)
D \(x^2-12x-144=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-144=0\)
Step 1
Concept
\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-144) gives (x^2-144=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-144=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-144) gives (x^2-144=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-144) रखने पर (x^2-144=0) मिलता है\)।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि (x=-2) समीकरण \(kx^2+5x+6=0\) का मूल नहीं है, तो (k) पर कौन-सी शर्त होगी?
If (x=-2) is not a root of \(kx^2+5x+6=0\), what condition must (k) satisfy?
#quadratic-equations
#not-root
#parameter
#expert
A \(k\neq1\)
B (k=1)
C \(k\neq2\)
D (k=2)
Explanation opens after your attempt
Correct Answer
A. \(k\neq1\)
Step 1
Concept
Putting (x=-2), the left side becomes (4k-10+6=4k-4). For it not to be a root, \(4k-4\neq0\), so \(k\neq1\).
Step 2
Why this answer is correct
The correct answer is A. \(k\neq1\). Putting (x=-2), the left side becomes (4k-10+6=4k-4). For it not to be a root, \(4k-4\neq0\), so \(k\neq1\).
Step 3
Exam Tip
(x=-2) रखने पर बायां पक्ष (4k-10+6=4k-4) होता है। मूल न होने के लिए \(4k-4\neq0\), इसलिए \(k\neq1\)।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2+px+36=0\) के मूल समान और धनात्मक हैं। (p) का मान क्या होगा?
The roots of \(x^2+px+36=0\) are equal and positive. What is the value of (p)?
#quadratic-equations
#equal-positive-roots
#parameter
#expert
A (-12)
B (12)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(p^2-144=0\) gives \(p=\pm12\). For equal positive roots, \(-\frac{p}{2}>0\), so (p=-12).
Step 2
Why this answer is correct
The correct answer is A. (-12). For equal roots, \(p^2-144=0\) gives \(p=\pm12\). For equal positive roots, \(-\frac{p}{2}>0\), so (p=-12).
Step 3
Exam Tip
समान मूलों के लिए \(p^2-144=0\) से \(p=\pm12\) मिलता है। धनात्मक समान मूल के लिए \(-\frac{p}{2}>0\), इसलिए (p=-12)।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2+mx+49=0\) का एक मूल दूसरे का व्युत्क्रम है, तो (m) के बारे में क्या कहा जा सकता है?
If one root of \(x^2+mx+49=0\) is the reciprocal of the other, what can be said about (m)?
#quadratic-equations
#reciprocal-roots
#conceptual
#expert
A ऐसा संभव नहीं है / It is not possible
B (m=49)
C (m=-49)
D (m=0)
Explanation opens after your attempt
Correct Answer
A. ऐसा संभव नहीं है / It is not possible
Step 1
Concept
If one root is the reciprocal of the other, the product of roots must be (1). Here the product is (49), so it is not possible.
Step 2
Why this answer is correct
The correct answer is A. ऐसा संभव नहीं है / It is not possible. If one root is the reciprocal of the other, the product of roots must be (1). Here the product is (49), so it is not possible.
Step 3
Exam Tip
एक मूल दूसरे का व्युत्क्रम हो तो मूलों का गुणनफल (1) होना चाहिए। यहाँ गुणनफल (49) है, इसलिए ऐसा संभव नहीं है।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(25x^2+40kx+16k^2=0\) के मूलों की प्रकृति क्या है?
What is the nature of roots of \(25x^2+40kx+16k^2=0\)?
#quadratic-equations
#perfect-square
#nature-of-roots
#expert
A दो समान वास्तविक मूल / Two equal real roots
B दो भिन्न वास्तविक मूल / Two distinct real roots
C कोई वास्तविक मूल नहीं / No real roots
D निर्धारित नहीं हो सकता / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. दो समान वास्तविक मूल / Two equal real roots
Step 1
Concept
It can be written as ((5x+4k)2 =0). Therefore both roots are equal and real.
Step 2
Why this answer is correct
The correct answer is A. दो समान वास्तविक मूल / Two equal real roots. It can be written as ((5x+4k)2 =0). Therefore both roots are equal and real.
Step 3
Exam Tip
यह ((5x+4k)2 =0) के रूप में लिखा जा सकता है। इसलिए दोनों मूल समान वास्तविक होते हैं।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि ((x+a)2 =x-2 -20x+100) है, तो (a) का मान क्या होगा?
If ((x+a)2 =x-2 -20x+100), what is the value of (a)?
#quadratic-equations
#identity
#coefficient-comparison
#expert
A (-10)
B (10)
C (-20)
D (100)
Explanation opens after your attempt
Step 1
Concept
((x+a)2 =x-2 +2ax+a-2 ). From (2a=-20), we get (a=-10).
Step 2
Why this answer is correct
The correct answer is A. (-10). ((x+a)2 =x-2 +2ax+a-2 ). From (2a=-20), we get (a=-10).
Step 3
Exam Tip
((x+a)2 =x-2 +2ax+a-2 ) होता है। (2a=-20) से (a=-10) मिलता है।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-13x+42=0\) के मूल \(\alpha,\beta\) हैं, तो \(\frac{1}{\alpha}+\frac{1}{\beta}\) क्या है?
If \(\alpha,\beta\) are roots of \(x^2-13x+42=0\), what is \(\frac{1}{\alpha}+\frac{1}{\beta}\)?
#quadratic-equations
#reciprocal-roots
#expert
A \( \frac{13}{42} \)
B \( \frac{42}{13} \)
C (13)
D (42)
Explanation opens after your attempt
Correct Answer
A. \( \frac{13}{42} \)
Step 1
Concept
\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\). Here the value is \(\frac{13}{42}\).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{13}{42} \). \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\). Here the value is \(\frac{13}{42}\).
Step 3
Exam Tip
\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\) होता है। यहाँ मान \(\frac{13}{42}\) है।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
दो संख्याओं का योग (17) और गुणनफल (72) है। वे किस द्विघात समीकरण के मूल हो सकते हैं?
Two numbers have sum (17) and product (72). They can be roots of which quadratic equation?
#quadratic-equations
#forming-equation
#sum-product
#expert
A \(x^2-17x+72=0\)
B \(x^2+17x+72=0\)
C \(x^2-72x+17=0\)
D \(x^2+72x-17=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-17x+72=0\)
Step 1
Concept
If the sum of roots is (17) and product is (72), the equation is \(x^2-17x+72=0\). Remember the monic form formula.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-17x+72=0\). If the sum of roots is (17) and product is (72), the equation is \(x^2-17x+72=0\). Remember the monic form formula.
Step 3
Exam Tip
यदि मूलों का योग (17) और गुणनफल (72) है, तो समीकरण \(x^2-17x+72=0\) होगा। मोनिक रूप का सूत्र याद रखें।
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Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
एक आयत की लंबाई (x+9) और चौड़ाई (x-6) है। क्षेत्रफल (130) हो तो सही समीकरण कौन-सा है?
A rectangle has length (x+9) and breadth (x-6). If its area is (130), which equation is correct?
#quadratic-equations
#word-problem
#area
#expert
A \(x^2+3x-184=0\)
B \(x^2+3x-130=0\)
C \(x^2-3x-184=0\)
D \(x^2+15x-184=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x-184=0\)
Step 1
Concept
The area is ((x+9)(x-6)=130). Expanding gives \(x^2+3x-54=130\), so \(x^2+3x-184=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x-184=0\). The area is ((x+9)(x-6)=130). Expanding gives \(x^2+3x-54=130\), so \(x^2+3x-184=0\).
Step 3
Exam Tip
क्षेत्रफल ((x+9)(x-6)=130) होगा। विस्तार से \(x^2+3x-54=130\), इसलिए \(x^2+3x-184=0\)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किस विकल्प में मूलों का योग ऋणात्मक और गुणनफल ऋणात्मक होगा?
In which option will the sum of roots be negative and the product of roots be negative?
#quadratic-equations
#sum-product
#signs
#expert
A \(x^2+5x-24=0\)
B \(x^2-5x-24=0\)
C \(x^2+5x+24=0\)
D \(x^2-5x+24=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+5x-24=0\)
Step 1
Concept
In the first option, the sum is \(-\frac{b}{a}=-5\) and the product is \(\frac{c}{a}=-24\). So both are negative.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+5x-24=0\). In the first option, the sum is \(-\frac{b}{a}=-5\) and the product is \(\frac{c}{a}=-24\). So both are negative.
Step 3
Exam Tip
पहले विकल्प में योग \(-\frac{b}{a}=-5\) और गुणनफल \(\frac{c}{a}=-24\) है। इसलिए दोनों ऋणात्मक हैं।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि समीकरण \(x^2+bx+100=0\) के दोनों मूल समान हैं और उनका मान (-10) है, तो (b) क्या है?
If both roots of \(x^2+bx+100=0\) are equal and their value is (-10), what is (b)?
#quadratic-equations
#equal-roots
#coefficient
#expert
A (20)
B (-20)
C (10)
D (-10)
Explanation opens after your attempt
Step 1
Concept
Both roots are (-10), so the sum is (-20). Here the sum of roots is (-b), so (b=20).
Step 2
Why this answer is correct
The correct answer is A. (20). Both roots are (-10), so the sum is (-20). Here the sum of roots is (-b), so (b=20).
Step 3
Exam Tip
दोनों मूल (-10) हैं, इसलिए योग (-20) है। यहाँ मूलों का योग (-b) है, अतः (b=20)।
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Question
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-18x+c=0\) पूर्ण वर्ग द्विघात समीकरण है, तो (c) का मान क्या होगा?
If \(x^2-18x+c=0\) is a perfect square quadratic equation, what is the value of (c)?
#quadratic-equations
#perfect-square
#parameter
#expert
A (81)
B (18)
C (36)
D (324)
Explanation opens after your attempt
Step 1
Concept
For a perfect square, (x-2 -18x+c=(x-9)2 ) is needed. Hence (c=81).
Step 2
Why this answer is correct
The correct answer is A. (81). For a perfect square, (x-2 -18x+c=(x-9)2 ) is needed. Hence (c=81).
Step 3
Exam Tip
पूर्ण वर्ग के लिए (x-2 -18x+c=(x-9)2 ) होना चाहिए। इसलिए (c=81) होगा।
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