Question 391/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(9x^2-12x+4=0\) का विवेचक (D) क्या है?
What is the discriminant (D) of \(9x^2-12x+4=0\)?
#quadratic-equations
#discriminant
#equal-roots
#medium
A (0)
B (12)
C (24)
D (-12)
Explanation opens after your attempt
Step 1
Concept
Here (D=(-12)2 -4\cdot9\cdot4=144-144=0). Even if (b) is negative, \(b^2\) is positive.
Step 2
Why this answer is correct
The correct answer is A. (0). Here (D=(-12)2 -4\cdot9\cdot4=144-144=0). Even if (b) is negative, \(b^2\) is positive.
Step 3
Exam Tip
यहाँ (D=(-12)2 -4\cdot9\cdot4=144-144=0) है। (b) ऋणात्मक हो तो भी \(b^2\) धनात्मक होता है।
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Question 392/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि (a=5), (b=-11), (c=-6) हैं, तो संबंधित द्विघात समीकरण कौन-सा है?
If (a=5), (b=-11), (c=-6), which is the corresponding quadratic equation?
#quadratic-equations
#forming-equation
#coefficients
#medium
A \(5x^2+11x-6=0\)
B \(5x^2-11x-6=0\)
C \(6x^2-11x-5=0\)
D \(5x^2-6x-11=0\)
Explanation opens after your attempt
Correct Answer
B. \(5x^2-11x-6=0\)
Step 1
Concept
Substituting into \(ax^2+bx+c=0\) gives \(5x^2-11x-6=0\). Treat the negative sign as part of the coefficient.
Step 2
Why this answer is correct
The correct answer is B. \(5x^2-11x-6=0\). Substituting into \(ax^2+bx+c=0\) gives \(5x^2-11x-6=0\). Treat the negative sign as part of the coefficient.
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(5x^2-11x-6=0\) मिलता है। ऋण चिन्ह को गुणांक का भाग मानें।
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Question 393/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण ((x+4)2 =5x+10) का मानक रूप कौन-सा है?
What is the standard form of ((x+4)2 =5x+10)?
#quadratic-equations
#identity
#standard-form
#medium
A \(x^2+3x+6=0\)
B \(x^2+8x+26=0\)
C \(x^2+13x+6=0\)
D \(x^2+3x-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x+6=0\)
Step 1
Concept
((x+4)2 =x-2 +8x+16), and subtracting (5x+10) gives \(x^2+3x+6=0\). Keep the middle term correct in square identities.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x+6=0\). ((x+4)2 =x-2 +8x+16), and subtracting (5x+10) gives \(x^2+3x+6=0\). Keep the middle term correct in square identities.
Step 3
Exam Tip
((x+4)2 =x-2 +8x+16) है और (5x+10) हटाने पर \(x^2+3x+6=0\) मिलता है। वर्ग सूत्र में मध्य पद सही रखें।
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Question 394/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
कौन-सा समीकरण द्विघात है लेकिन अभी मानक रूप में नहीं है?
Which equation is quadratic but not yet in standard form?
#quadratic-equations
#identify
#standard-form
#medium
A \(4x^2-3x+1=0\)
B \(4x^2+1=3x\)
C (4x+1=3)
D \(x^3+1=3x\)
Explanation opens after your attempt
Correct Answer
B. \(4x^2+1=3x\)
Step 1
Concept
\(4x^2+1=3x\) can be written as \(4x^2-3x+1=0\). In standard form, all terms are on one side and (0) is on the other.
Step 2
Why this answer is correct
The correct answer is B. \(4x^2+1=3x\). \(4x^2+1=3x\) can be written as \(4x^2-3x+1=0\). In standard form, all terms are on one side and (0) is on the other.
Step 3
Exam Tip
\(4x^2+1=3x\) को \(4x^2-3x+1=0\) लिखा जा सकता है। मानक रूप में सभी पद एक ओर और दूसरी ओर (0) होता है।
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Question 395/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि (x=3) समीकरण \(2x^2+qx-15=0\) का मूल है, तो (q) का मान क्या होगा?
If (x=3) is a root of \(2x^2+qx-15=0\), what is the value of (q)?
#quadratic-equations
#parameter
#root
#medium
A (1)
B (-1)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
Putting (x=3) gives (18+3q-15=0), so (q=-1). If a root is given, substitute it into the equation.
Step 2
Why this answer is correct
The correct answer is B. (-1). Putting (x=3) gives (18+3q-15=0), so (q=-1). If a root is given, substitute it into the equation.
Step 3
Exam Tip
(x=3) रखने पर (18+3q-15=0), इसलिए (q=-1) है। मूल दिया हो तो उसे समीकरण में रखें।
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Question 396/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
क्या (x=-1) समीकरण \(x^2+5x+4=0\) का मूल है?
Is (x=-1) a root of \(x^2+5x+4=0\)?
#quadratic-equations
#root-check
#substitution
#medium
A हाँ / Yes
B नहीं / No
C केवल (x=4) मूल है / Only (x=4) is a root
D निर्धारित नहीं किया जा सकता / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=-1) gives (1-5+4=0). To check a root, substitute the given value directly.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=-1) gives (1-5+4=0). To check a root, substitute the given value directly.
Step 3
Exam Tip
(x=-1) रखने पर (1-5+4=0) मिलता है। मूल की जांच के लिए दिए मान को सीधे रखें।
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Question 397/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(8x-x^2=15\) का मानक रूप कौन-सा है जिसमें \(x^2\) का गुणांक धनात्मक हो?
What is the standard form of \(8x-x^2=15\) with positive coefficient of \(x^2\)?
#quadratic-equations
#standard-form
#transposition
#medium
A \(x^2-8x+15=0\)
B \(x^2+8x-15=0\)
C \(x^2-8x-15=0\)
D \(x^2+8x+15=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-8x+15=0\)
Step 1
Concept
Bringing all terms to one side gives \(-x^2+8x-15=0\). Multiplying by (-1) gives \(x^2-8x+15=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-8x+15=0\). Bringing all terms to one side gives \(-x^2+8x-15=0\). Multiplying by (-1) gives \(x^2-8x+15=0\).
Step 3
Exam Tip
सभी पद एक ओर लाने पर \(-x^2+8x-15=0\) मिलता है। (-1) से गुणा करने पर \(x^2-8x+15=0\) मिलता है।
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Question 398/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(-4x^2+6x-9=0\) के लिए (a-b+c) का मान क्या है?
For the equation \(-4x^2+6x-9=0\), what is the value of (a-b+c)?
#quadratic-equations
#coefficients
#signs
#medium
A (1)
B (-19)
C (11)
D (-7)
Explanation opens after your attempt
Step 1
Concept
Here (a=-4), (b=6), (c=-9). Hence (a-b+c=-4-6-9=-19).
Step 2
Why this answer is correct
The correct answer is B. (-19). Here (a=-4), (b=6), (c=-9). Hence (a-b+c=-4-6-9=-19).
Step 3
Exam Tip
यहाँ (a=-4), (b=6), (c=-9) हैं। इसलिए (a-b+c=-4-6-9=-19) है।
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Question 399/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि ((2m-3)x-2 +7x-1=0) द्विघात समीकरण है, तो (m) के लिए सही शर्त क्या है?
If ((2m-3)x-2 +7x-1=0) is a quadratic equation, what is the correct condition for (m)?
#quadratic-equations
#parameter
#condition
#medium
A \(m=\frac{3}{2}\)
B \(m\neq \frac{3}{2}\)
C \(m\neq -\frac{3}{2}\)
D (m=0)
Explanation opens after your attempt
Correct Answer
B. \(m\neq \frac{3}{2}\)
Step 1
Concept
For a quadratic equation, the coefficient of \(x^2\) must not be (0). Thus \(2m-3\neq 0\), so \(m\neq \frac{3}{2}\).
Step 2
Why this answer is correct
The correct answer is B. \(m\neq \frac{3}{2}\). For a quadratic equation, the coefficient of \(x^2\) must not be (0). Thus \(2m-3\neq 0\), so \(m\neq \frac{3}{2}\).
Step 3
Exam Tip
द्विघात होने के लिए \(x^2\) का गुणांक (0) नहीं होना चाहिए। इसलिए \(2m-3\neq 0\), अर्थात \(m\neq \frac{3}{2}\)।
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Question 400/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण ((3x+2)(x-5)=0) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of ((3x+2)(x-5)=0)?
#quadratic-equations
#standard-form
#expansion
#medium
A \(3x^2-13x-10=0\)
B \(3x^2+13x-10=0\)
C \(3x^2-15x+2=0\)
D \(3x^2+17x+10=0\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-13x-10=0\)
Step 1
Concept
Expanding ((3x+2)(x-5)) gives \(3x^2-15x+2x-10\). So the standard form is \(3x^2-13x-10=0\).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-13x-10=0\). Expanding ((3x+2)(x-5)) gives \(3x^2-15x+2x-10\). So the standard form is \(3x^2-13x-10=0\).
Step 3
Exam Tip
((3x+2)(x-5)) को फैलाने पर \(3x^2-15x+2x-10\) मिलता है। इसलिए मानक रूप \(3x^2-13x-10=0\) है।
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Question 401/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण ((x+3)2 =2x+15) का मानक रूप कौन-सा है?
What is the standard form of ((x+3)2 =2x+15)?
#quadratic-equations
#standard-form
#identity
#medium
A \(x^2+4x-6=0\)
B \(x^2+8x-6=0\)
C \(x^2+4x+6=0\)
D \(x^2+6x-15=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x-6=0\)
Step 1
Concept
Here ((x+3)2 =x-2 +6x+9), and bringing all terms to one side gives \(x^2+4x-6=0\). Use the square identity and transposition carefully.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4x-6=0\). Here ((x+3)2 =x-2 +6x+9), and bringing all terms to one side gives \(x^2+4x-6=0\). Use the square identity and transposition carefully.
Step 3
Exam Tip
((x+3)2 =x-2 +6x+9) है और सभी पद एक ओर लाने पर \(x^2+4x-6=0\) मिलता है। वर्ग सूत्र और स्थानांतरण दोनों सावधानी से करें।
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Question 402/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(x^2-4x+4=0\) को किस पूर्ण वर्ग रूप में लिखा जा सकता है?
In which perfect square form can \(x^2-4x+4=0\) be written?
#quadratic-equations
#perfect-square
#identity
#medium
A ((x-2)2 =0)
B ((x+2)2 =0)
C ((x-4)2 =0)
D ((x+4)2 =0)
Explanation opens after your attempt
Correct Answer
A. ((x-2)2 =0)
Step 1
Concept
(x-2 -4x+4=(x-2)2 ). To identify a perfect square, match the middle term with (2ab).
Step 2
Why this answer is correct
The correct answer is A. ((x-2)2 =0). (x-2 -4x+4=(x-2)2 ). To identify a perfect square, match the middle term with (2ab).
Step 3
Exam Tip
(x-2 -4x+4=(x-2)2 ) होता है। पूर्ण वर्ग पहचानने के लिए मध्य पद (2ab) से मिलाएं।
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Question 403/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
एक वर्ग का क्षेत्रफल उसकी भुजा के (6) गुने से (7) अधिक है। यदि भुजा (x) है, तो समीकरण कौन-सा है?
The area of a square is (7) more than (6) times its side. If the side is (x), which equation is correct?
#quadratic-equations
#word-problem
#square-area
#medium
A \(x^2-6x-7=0\)
B \(x^2+6x+7=0\)
C \(x^2-7x-6=0\)
D \(6x^2-x+7=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-6x-7=0\)
Step 1
Concept
The area is \(x^2\) and it is given that \(x^2=6x+7\). Therefore \(x^2-6x-7=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-6x-7=0\). The area is \(x^2\) and it is given that \(x^2=6x+7\). Therefore \(x^2-6x-7=0\) is correct.
Step 3
Exam Tip
क्षेत्रफल \(x^2\) है और दिया है \(x^2=6x+7\)। इसलिए \(x^2-6x-7=0\) सही है।
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Question 404/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि \(x^2+ax+10=0\) के मूल (-2) और (-5) हैं, तो (a) का मान क्या है?
If the roots of \(x^2+ax+10=0\) are (-2) and (-5), what is the value of (a)?
#quadratic-equations
#parameter
#roots
#medium
A (7)
B (-7)
C (10)
D (-10)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (-7), and in \(x^2+ax+10=0\) the sum is (-a). Therefore (a=7).
Step 2
Why this answer is correct
The correct answer is A. (7). The sum of roots is (-7), and in \(x^2+ax+10=0\) the sum is (-a). Therefore (a=7).
Step 3
Exam Tip
मूलों का योग (-7) है और \(x^2+ax+10=0\) में योग (-a) होता है। इसलिए (a=7) है।
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Question 405/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(x^2-11x+30=0\) में मूलों की पहचान के लिए कौन-सी संख्या जोड़ी उपयोगी है?
Which pair of numbers is useful to identify the roots of \(x^2-11x+30=0\)?
#quadratic-equations
#factorisation
#number-pair
#medium
A (5) और (6) / (5) and (6)
B (3) और (10) / (3) and (10)
C (2) और (15) / (2) and (15)
D (1) और (30) / (1) and (30)
Explanation opens after your attempt
Correct Answer
A. (5) और (6) / (5) and (6)
Step 1
Concept
\(5\cdot6=30\) and (5+6=11). Because the middle term is negative, the factors are ((x-5)(x-6)).
Step 2
Why this answer is correct
The correct answer is A. (5) और (6) / (5) and (6). \(5\cdot6=30\) and (5+6=11). Because the middle term is negative, the factors are ((x-5)(x-6)).
Step 3
Exam Tip
\(5\cdot6=30\) और (5+6=11) होता है। ऋण मध्य पद के कारण गुणनखंड ((x-5)(x-6)) बनते हैं।
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Question 406/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि \(3x^2-12x+12=0\) को (3) से भाग दें, तो सरल समीकरण कौन-सा होगा?
If \(3x^2-12x+12=0\) is divided by (3), which simplified equation is obtained?
#quadratic-equations
#simplification
#common-factor
#medium
A \(x^2-4x+4=0\)
B \(x^2+4x+4=0\)
C \(3x^2-4x+4=0\)
D \(x^2-12x+12=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x+4=0\)
Step 1
Concept
Dividing every term by (3) gives \(x^2-4x+4=0\). Dividing by a common nonzero factor does not change the roots.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x+4=0\). Dividing every term by (3) gives \(x^2-4x+4=0\). Dividing by a common nonzero factor does not change the roots.
Step 3
Exam Tip
हर पद को (3) से भाग देने पर \(x^2-4x+4=0\) मिलता है। समान गुणनखंड से भाग देने पर मूल नहीं बदलते।
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Question 407/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
किस विकल्प में द्विघात समीकरण का (x) वाला पद अनुपस्थित है लेकिन समीकरण द्विघात है?
In which option is the (x) term absent but the equation is still quadratic?
#quadratic-equations
#missing-linear-term
#pure-quadratic
#medium
A \(x^2-49=0\)
B (7x-49=0)
C \(x^3-49=0\)
D \(\frac{1}{x^2}-49=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-49=0\)
Step 1
Concept
In \(x^2-49=0\), the \(x^2\) term is present and the (x) term is absent. An equation can be quadratic even without an (x) term.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-49=0\). In \(x^2-49=0\), the \(x^2\) term is present and the (x) term is absent. An equation can be quadratic even without an (x) term.
Step 3
Exam Tip
\(x^2-49=0\) में \(x^2\) पद है और (x) पद अनुपस्थित है। (x) पद न होने पर भी समीकरण द्विघात हो सकता है।
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Question 408/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(x^2+kx+25=0\) में यदि मूल समान और ऋणात्मक हैं, तो (k) का संभव मान कौन-सा है?
In \(x^2+kx+25=0\), if the roots are equal and negative, which possible value of (k) is correct?
#quadratic-equations
#equal-negative-roots
#parameter
#medium
A (10)
B (-10)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0) gives \(k^2=100\), and for equal negative roots \(-\frac{k}{2}<0\) is needed. Hence (k=10) is correct.
Step 2
Why this answer is correct
The correct answer is A. (10). For equal roots, (D=0) gives \(k^2=100\), and for equal negative roots \(-\frac{k}{2}<0\) is needed. Hence (k=10) is correct.
Step 3
Exam Tip
समान मूलों के लिए (D=0) से \(k^2=100\), और ऋणात्मक समान मूल के लिए \(-\frac{k}{2}<0\) चाहिए। इसलिए (k=10) सही है।
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Question 409/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि द्विघात समीकरण \(x^2-6x+k=0\) के मूल समान हैं, तो (k) क्या होगा?
If the roots of \(x^2-6x+k=0\) are equal, what is (k)?
#quadratic-equations
#equal-roots
#discriminant
#medium
A (6)
B (9)
C (12)
D (36)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (36-4k=0) and (k=9). Set the discriminant to zero for equal roots.
Step 2
Why this answer is correct
The correct answer is B. (9). For equal roots, (D=0), so (36-4k=0) and (k=9). Set the discriminant to zero for equal roots.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (36-4k=0) और (k=9)। समान मूल की शर्त में विवेचक शून्य रखें।
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Question 410/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
किस समीकरण के दोनों मूल विपरीत संख्याएँ होंगे?
Which equation will have roots that are opposite numbers?
#quadratic-equations
#opposite-roots
#pure-quadratic
#medium
A \(x^2-16=0\)
B \(x^2+4x+4=0\)
C \(x^2-5x+6=0\)
D \(x^2+x-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-16=0\)
Step 1
Concept
\(x^2-16=0\) gives \(x=\pm4\), which are opposite numbers. Pure quadratics often give opposite roots.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-16=0\). \(x^2-16=0\) gives \(x=\pm4\), which are opposite numbers. Pure quadratics often give opposite roots.
Step 3
Exam Tip
\(x^2-16=0\) से \(x=\pm4\) मिलता है, जो विपरीत संख्याएँ हैं। शुद्ध द्विघात में अक्सर विपरीत मूल मिलते हैं।
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Question 411/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि \(x^2-9x+20=0\), तो (x=4) रखने पर बायां पक्ष क्या बनेगा?
If \(x^2-9x+20=0\), what will the left side become when (x=4)?
#quadratic-equations
#substitution
#root-verification
#medium
A (0)
B (4)
C (-4)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(4^2-9\cdot4+20=16-36+20=0\). If the left side becomes (0), the given value is a root.
Step 2
Why this answer is correct
The correct answer is A. (0). \(4^2-9\cdot4+20=16-36+20=0\). If the left side becomes (0), the given value is a root.
Step 3
Exam Tip
\(4^2-9\cdot4+20=16-36+20=0\) है। यदि बायां पक्ष (0) हो तो दिया मान मूल होता है।
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Question 412/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण ((x-1)(x+6)=2x) का मानक रूप क्या है?
What is the standard form of ((x-1)(x+6)=2x)?
#quadratic-equations
#standard-form
#expansion
#medium
A \(x^2+3x-6=0\)
B \(x^2+5x-6=0\)
C \(x^2+7x-6=0\)
D \(x^2-3x-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x-6=0\)
Step 1
Concept
The left side gives \(x^2+5x-6\), and subtracting (2x) gives \(x^2+3x-6=0\). First expand and then bring all terms to one side.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x-6=0\). The left side gives \(x^2+5x-6\), and subtracting (2x) gives \(x^2+3x-6=0\). First expand and then bring all terms to one side.
Step 3
Exam Tip
बाईं ओर \(x^2+5x-6\) मिलता है, फिर (2x) घटाने पर \(x^2+3x-6=0\) बनता है। पहले फैलाएं फिर सभी पद एक ओर लाएं।
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Question 413/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण ((x+2)2 -(x+2)-6=0) को सरल करने पर कौन-सा द्विघात समीकरण मिलेगा?
Which quadratic equation is obtained by simplifying ((x+2)2 -(x+2)-6=0)?
#quadratic-equations
#simplification
#identity
#medium
A \(x^2+3x-4=0\)
B \(x^2+4x-2=0\)
C \(x^2+3x+4=0\)
D \(x^2+5x=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x-4=0\)
Step 1
Concept
((x+2)2 =x-2 +4x+4), so the simplified form is \(x^2+3x-4=0\). Write every term while opening brackets.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x-4=0\). ((x+2)2 =x-2 +4x+4), so the simplified form is \(x^2+3x-4=0\). Write every term while opening brackets.
Step 3
Exam Tip
((x+2)2 =x-2 +4x+4) है, इसलिए सरल रूप \(x^2+3x-4=0\) है। कोष्ठक खोलते समय हर पद लिखें।
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Question 414/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि \(x^2+px+16=0\) के मूल (4) और (4) हैं, तो (p) का मान क्या होगा?
If the roots of \(x^2+px+16=0\) are (4) and (4), what is the value of (p)?
#quadratic-equations
#equal-roots
#parameter
#medium
A (8)
B (-8)
C (16)
D (-16)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (8), and in \(x^2+px+16=0\) the sum is (-p). Therefore (p=-8).
Step 2
Why this answer is correct
The correct answer is B. (-8). The sum of roots is (8), and in \(x^2+px+16=0\) the sum is (-p). Therefore (p=-8).
Step 3
Exam Tip
मूलों का योग (8) है और \(x^2+px+16=0\) में योग (-p) होता है। इसलिए (p=-8) है।
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Question 415/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(x^2-2x-15=0\) के मूलों में से कौन-सा सही युग्म है?
Which pair is the correct roots of \(x^2-2x-15=0\)?
#quadratic-equations
#roots
#factorisation
#medium
A (3,-5)
B (5,-3)
C (-5,-3)
D (5,3)
Explanation opens after your attempt
Step 1
Concept
From ((x-5)(x+3)=0), the roots are (5) and (-3). Match both product and sum in such questions.
Step 2
Why this answer is correct
The correct answer is B. (5,-3). From ((x-5)(x+3)=0), the roots are (5) and (-3). Match both product and sum in such questions.
Step 3
Exam Tip
((x-5)(x+3)=0) से मूल (5) और (-3) मिलते हैं। ऐसे प्रश्नों में गुणनफल और योग दोनों मिलाएं।
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Question 416/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
किस समीकरण में (x=1) मूल नहीं है?
In which equation is (x=1) not a root?
#quadratic-equations
#root-check
#not-root
#medium
A \(x^2-1=0\)
B \(x^2-3x+2=0\)
C \(2x^2+x-3=0\)
D \(x^2+x+1=0\)
Explanation opens after your attempt
Correct Answer
D. \(x^2+x+1=0\)
Step 1
Concept
Putting (x=1) gives \(1+1+1=3\neq 0\). To check when a value is not a root, use substitution too.
Step 2
Why this answer is correct
The correct answer is D. \(x^2+x+1=0\). Putting (x=1) gives \(1+1+1=3\neq 0\). To check when a value is not a root, use substitution too.
Step 3
Exam Tip
(x=1) रखने पर \(1+1+1=3\neq 0\) मिलता है। किसी विकल्प में मूल न होने की जांच भी प्रतिस्थापन से करें।
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Question 417/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि \(kx^2-4x+2=0\) में मूलों का गुणनफल (1) है, तो (k) का मान क्या है?
If the product of roots of \(kx^2-4x+2=0\) is (1), what is the value of (k)?
#quadratic-equations
#parameter
#product-of-roots
#medium
A (1)
B (2)
C (-2)
D (4)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{2}{k}=1\), so (k=2). Use (c/a) for the product formula.
Step 2
Why this answer is correct
The correct answer is B. (2). The product of roots is \(\frac{2}{k}=1\), so (k=2). Use (c/a) for the product formula.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{2}{k}=1\), इसलिए (k=2) है। गुणनफल के सूत्र में (c/a) प्रयोग करें।
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Question 418/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि \(2x^2+mx+8=0\) में मूलों का योग (-3) है, तो (m) क्या है?
If the sum of roots of \(2x^2+mx+8=0\) is (-3), what is (m)?
#quadratic-equations
#parameter
#sum-of-roots
#medium
A (6)
B (-6)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is \(-\frac{m}{2}=-3\), so (m=6). Notice the negative sign in the sum formula.
Step 2
Why this answer is correct
The correct answer is A. (6). The sum of roots is \(-\frac{m}{2}=-3\), so (m=6). Notice the negative sign in the sum formula.
Step 3
Exam Tip
मूलों का योग \(-\frac{m}{2}=-3\), इसलिए (m=6) है। योग के सूत्र में ऋण चिन्ह पर ध्यान दें।
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Question 419/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(3x^2+2x-8=0\) में मूलों का गुणनफल क्या है?
What is the product of roots of \(3x^2+2x-8=0\)?
#quadratic-equations
#product-of-roots
#medium
A \(-\frac{8}{3}\)
B \(\frac{8}{3}\)
C \(-\frac{2}{3}\)
D \(\frac{2}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{8}{3}\)
Step 1
Concept
The product of roots is \(\frac{c}{a}=\frac{-8}{3}\). Use the sign of (c) directly in the formula.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{8}{3}\). The product of roots is \(\frac{c}{a}=\frac{-8}{3}\). Use the sign of (c) directly in the formula.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}=\frac{-8}{3}\) है। (c) का चिन्ह सीधे सूत्र में रखें।
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Question 420/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(2x^2-5x+3=0\) में मूलों का योग क्या है?
What is the sum of roots of \(2x^2-5x+3=0\)?
#quadratic-equations
#sum-of-roots
#medium
A \(\frac{5}{2}\)
B \(-\frac{5}{2}\)
C \(\frac{3}{2}\)
D \(-\frac{3}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{5}{2}\)
Step 1
Concept
The sum of roots is \(-\frac{b}{a}=-\frac{-5}{2}=\frac{5}{2}\). Pay attention to the sign of (b) in the formula.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{5}{2}\). The sum of roots is \(-\frac{b}{a}=-\frac{-5}{2}=\frac{5}{2}\). Pay attention to the sign of (b) in the formula.
Step 3
Exam Tip
मूलों का योग \(-\frac{b}{a}=-\frac{-5}{2}=\frac{5}{2}\) है। सूत्र में (b) का चिन्ह ध्यान से रखें।
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