Question 361/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-12x+35=0\), तो (x=5) रखने पर बायां पक्ष क्या बनेगा?
If \(x^2-12x+35=0\), what will the left side become when (x=5)?
#quadratic-equations
#substitution
#root-verification
#medium
A (0)
B (5)
C (-5)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(5^2-12\cdot5+35=25-60+35=0\). 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). \(5^2-12\cdot5+35=25-60+35=0\). If the left side becomes (0), the given value is a root.
Step 3
Exam Tip
\(5^2-12\cdot5+35=25-60+35=0\) है। बायां पक्ष (0) हो तो दिया मान मूल है।
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Question 362/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण ((x+2)(x-7)=3x) का मानक रूप क्या है?
What is the standard form of ((x+2)(x-7)=3x)?
#quadratic-equations
#standard-form
#expansion
#medium
A \(x^2-8x-14=0\)
B \(x^2-5x-14=0\)
C \(x^2-2x-14=0\)
D \(x^2+8x-14=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-8x-14=0\)
Step 1
Concept
The left side gives \(x^2-5x-14\). Subtracting (3x) gives \(x^2-8x-14=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-8x-14=0\). The left side gives \(x^2-5x-14\). Subtracting (3x) gives \(x^2-8x-14=0\).
Step 3
Exam Tip
बाईं ओर \(x^2-5x-14\) मिलता है। (3x) को घटाने पर \(x^2-8x-14=0\) बनता है।
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Question 363/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण ((x-3)2 +2(x-3)-8=0) को सरल करने पर कौन-सा द्विघात समीकरण मिलेगा?
Which quadratic equation is obtained by simplifying ((x-3)2 +2(x-3)-8=0)?
#quadratic-equations
#simplification
#identity
#medium
A \(x^2-4x-5=0\)
B \(x^2+4x-5=0\)
C \(x^2-6x+1=0\)
D \(x^2-4x+5=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x-5=0\)
Step 1
Concept
((x-3)2 =x-2 -6x+9) and (2(x-3)=2x-6). Simplifying gives \(x^2-4x-5=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x-5=0\). ((x-3)2 =x-2 -6x+9) and (2(x-3)=2x-6). Simplifying gives \(x^2-4x-5=0\).
Step 3
Exam Tip
((x-3)2 =x-2 -6x+9) है और (2(x-3)=2x-6) है। सरल करने पर \(x^2-4x-5=0\) मिलता है।
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Question 364/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2+rx+36=0\) के मूल (6) और (6) हैं, तो (r) का मान क्या होगा?
If the roots of \(x^2+rx+36=0\) are (6) and (6), what is the value of (r)?
#quadratic-equations
#equal-roots
#parameter
#medium
A (12)
B (-12)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (12), and in \(x^2+rx+36=0\) the sum is (-r). Therefore (r=-12).
Step 2
Why this answer is correct
The correct answer is B. (-12). The sum of roots is (12), and in \(x^2+rx+36=0\) the sum is (-r). Therefore (r=-12).
Step 3
Exam Tip
मूलों का योग (12) है और \(x^2+rx+36=0\) में योग (-r) होता है। इसलिए (r=-12) है।
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Question 365/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2+2x-35=0\) के मूलों का सही युग्म कौन-सा है?
Which pair is the correct roots of \(x^2+2x-35=0\)?
#quadratic-equations
#roots
#factorisation
#medium
A (5,-7)
B (7,-5)
C (-5,-7)
D (5,7)
Explanation opens after your attempt
Step 1
Concept
From ((x+7)(x-5)=0), the roots are (-7) and (5). Check both product and sum.
Step 2
Why this answer is correct
The correct answer is A. (5,-7). From ((x+7)(x-5)=0), the roots are (-7) and (5). Check both product and sum.
Step 3
Exam Tip
((x+7)(x-5)=0) से मूल (-7) और (5) मिलते हैं। गुणनफल और योग दोनों मिलाकर जांचें।
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Question 366/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किस समीकरण में (x=-2) मूल नहीं है?
In which equation is (x=-2) not a root?
#quadratic-equations
#root-check
#not-root
#medium
A \(x^2+2x=0\)
B \(x^2+5x+6=0\)
C \(2x^2+3x-2=0\)
D \(x^2-2x+4=0\)
Explanation opens after your attempt
Correct Answer
D. \(x^2-2x+4=0\)
Step 1
Concept
Putting (x=-2) gives \(4+4+4=12\neq0\). To check a non-root, use substitution too.
Step 2
Why this answer is correct
The correct answer is D. \(x^2-2x+4=0\). Putting (x=-2) gives \(4+4+4=12\neq0\). To check a non-root, use substitution too.
Step 3
Exam Tip
(x=-2) रखने पर \(4+4+4=12\neq0\) मिलता है। मूल न होने की जांच भी प्रतिस्थापन से करें।
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Question 367/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(px^2+6x+9=0\) में मूलों का गुणनफल (3) है, तो (p) का मान क्या है?
If the product of roots of \(px^2+6x+9=0\) is (3), what is the value of (p)?
#quadratic-equations
#parameter
#product-of-roots
#medium
A (3)
B (6)
C (9)
D (-3)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{9}{p}=3\), so (p=3). Use \(\frac{c}{a}\) for the product of roots.
Step 2
Why this answer is correct
The correct answer is A. (3). The product of roots is \(\frac{9}{p}=3\), so (p=3). Use \(\frac{c}{a}\) for the product of roots.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{9}{p}=3\), इसलिए (p=3) है। गुणनफल के लिए \(\frac{c}{a}\) का प्रयोग करें।
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Question 368/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(3x^2+nx+12=0\) में मूलों का योग (-4) है, तो (n) क्या है?
If the sum of roots of \(3x^2+nx+12=0\) is (-4), what is (n)?
#quadratic-equations
#parameter
#sum-of-roots
#medium
A (12)
B (-12)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is \(-\frac{n}{3}=-4\), so (n=12). Do not forget the negative sign in the sum formula.
Step 2
Why this answer is correct
The correct answer is A. (12). The sum of roots is \(-\frac{n}{3}=-4\), so (n=12). Do not forget the negative sign in the sum formula.
Step 3
Exam Tip
मूलों का योग \(-\frac{n}{3}=-4\), इसलिए (n=12) है। योग के सूत्र में ऋण चिन्ह न भूलें।
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Question 369/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(5x^2-3x-11=0\) में मूलों का गुणनफल क्या है?
What is the product of roots of \(5x^2-3x-11=0\)?
#quadratic-equations
#product-of-roots
#medium
A \(-\frac{11}{5}\)
B \(\frac{11}{5}\)
C \(-\frac{3}{5}\)
D \(\frac{3}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{11}{5}\)
Step 1
Concept
The product of roots is \(\frac{c}{a}=\frac{-11}{5}\). The sign of (c) is used directly in the formula.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{11}{5}\). The product of roots is \(\frac{c}{a}=\frac{-11}{5}\). The sign of (c) is used directly in the formula.
Step 3
Exam Tip
मूलों का गुणनफल \(\frac{c}{a}=\frac{-11}{5}\) है। (c) का चिन्ह सूत्र में सीधे आता है।
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Question 370/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(4x^2-7x+2=0\) में मूलों का योग क्या है?
What is the sum of roots of \(4x^2-7x+2=0\)?
#quadratic-equations
#sum-of-roots
#medium
A \(\frac{7}{4}\)
B \(-\frac{7}{4}\)
C \(\frac{1}{2}\)
D (2)
Explanation opens after your attempt
Correct Answer
A. \(\frac{7}{4}\)
Step 1
Concept
The sum of roots is \(-\frac{b}{a}=-\frac{-7}{4}=\frac{7}{4}\). Pay attention to the sign of (b) in the formula.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{7}{4}\). The sum of roots is \(-\frac{b}{a}=-\frac{-7}{4}=\frac{7}{4}\). Pay attention to the sign of (b) in the formula.
Step 3
Exam Tip
मूलों का योग \(-\frac{b}{a}=-\frac{-7}{4}=\frac{7}{4}\) है। सूत्र में (b) का चिन्ह ध्यान से रखें।
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Question 371/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किस द्विघात समीकरण में मूलों का योग (-6) और गुणनफल (8) है?
Which quadratic equation has sum of roots (-6) and product (8)?
#quadratic-equations
#sum-product
#forming-equation
#medium
A \(x^2+6x+8=0\)
B \(x^2-6x+8=0\)
C \(x^2+8x+6=0\)
D \(x^2-8x+6=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+6x+8=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-6) gives (x^2+6x+8=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+6x+8=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-6) gives (x^2+6x+8=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-6) रखने पर (x^2+6x+8=0) मिलता है\)।
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Question 372/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि मूल (-3) और (-8) हैं, तो मूलों का गुणनफल क्या है?
If the roots are (-3) and (-8), what is the product of the roots?
#quadratic-equations
#roots
#product
#medium
A (24)
B (-24)
C (11)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The product of roots is ((-3)(-8)=24). The product of two negative numbers is positive.
Step 2
Why this answer is correct
The correct answer is A. (24). The product of roots is ((-3)(-8)=24). The product of two negative numbers is positive.
Step 3
Exam Tip
मूलों का गुणनफल ((-3)(-8)=24) है। दो ऋणात्मक संख्याओं का गुणनफल धनात्मक होता है।
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Question 373/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि (x=-5) और (x=2) मूल हैं, तो मूलों का योग क्या है?
If (x=-5) and (x=2) are roots, what is the sum of the roots?
#quadratic-equations
#roots
#sum
#medium
A (-3)
B (3)
C (-7)
D (7)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (-5+2=-3). For numbers with opposite signs, the sign of the larger magnitude is used.
Step 2
Why this answer is correct
The correct answer is A. (-3). The sum of roots is (-5+2=-3). For numbers with opposite signs, the sign of the larger magnitude is used.
Step 3
Exam Tip
मूलों का योग (-5+2=-3) है। विपरीत चिन्ह वाली संख्याओं में बड़े परिमाण का चिन्ह आता है।
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Question 374/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2-4\sqrt{2}x+8=0\) में (b) का मान क्या है?
What is the value of (b) in \(x^2-4\sqrt{2}x+8=0\)?
#quadratic-equations
#coefficients
#radicals
#medium
A \(-4\sqrt{2}\)
B \(4\sqrt{2}\)
C (8)
D (1)
Explanation opens after your attempt
Correct Answer
A. \(-4\sqrt{2}\)
Step 1
Concept
The coefficient attached to (x) is \(-4\sqrt{2}\). Keep the sign with radical coefficients too.
Step 2
Why this answer is correct
The correct answer is A. \(-4\sqrt{2}\). The coefficient attached to (x) is \(-4\sqrt{2}\). Keep the sign with radical coefficients too.
Step 3
Exam Tip
(x) के साथ लगा गुणांक \(-4\sqrt{2}\) है। करणी वाले गुणांक में भी चिन्ह साथ रखें।
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Question 375/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
कौन-सा विकल्प सामान्य रूप में द्विघात समीकरण नहीं है?
Which option is not a quadratic equation in the usual form?
#quadratic-equations
#non-quadratic
#radical
#medium
A \(2x^2-5=0\)
B \(x^2+3x=0\)
C \(\sqrt{x}+x=4\)
D \(6x^2+x+1=0\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{x}+x=4\)
Step 1
Concept
The term \(\sqrt{x}\) has a fractional power of the variable, so it is not in usual quadratic form. Quadratic form has only \(x^2\), (x), and constant terms.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{x}+x=4\). The term \(\sqrt{x}\) has a fractional power of the variable, so it is not in usual quadratic form. Quadratic form has only \(x^2\), (x), and constant terms.
Step 3
Exam Tip
\(\sqrt{x}\) में चर की भिन्न घात है, इसलिए यह सामान्य द्विघात रूप नहीं है। द्विघात रूप में केवल \(x^2\), (x) और स्थिर पद होते हैं।
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Question 376/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(\frac{2}{5}x^2+\frac{1}{5}x-2=0\) का पूर्णांक गुणांकों वाला रूप कौन-सा है?
What is the form with integer coefficients for \(\frac{2}{5}x^2+\frac{1}{5}x-2=0\)?
#quadratic-equations
#fractional-coefficients
#medium
A \(2x^2+x-10=0\)
B \(2x^2+x-2=0\)
C \(5x^2+x-2=0\)
D \(2x^2+5x-10=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+x-10=0\)
Step 1
Concept
Multiply the whole equation by (5) to remove denominator (5). This gives \(2x^2+x-10=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+x-10=0\). Multiply the whole equation by (5) to remove denominator (5). This gives \(2x^2+x-10=0\).
Step 3
Exam Tip
हर (5) हटाने के लिए पूरे समीकरण को (5) से गुणा करें। इससे \(2x^2+x-10=0\) मिलता है।
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Question 377/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(\frac{x^2}{4}-x+3=0\) को बिना भिन्न के किस रूप में लिखा जाएगा?
How will \(\frac{x^2}{4}-x+3=0\) be written without fractions?
#quadratic-equations
#fractions
#standard-form
#medium
A \(x^2-4x+12=0\)
B \(x^2-x+12=0\)
C \(4x^2-x+3=0\)
D \(x^2+4x+12=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x+12=0\)
Step 1
Concept
Multiplying the whole equation by (4) gives \(x^2-4x+12=0\). To remove fractions, multiply the whole equation.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x+12=0\). Multiplying the whole equation by (4) gives \(x^2-4x+12=0\). To remove fractions, multiply the whole equation.
Step 3
Exam Tip
पूरे समीकरण को (4) से गुणा करने पर \(x^2-4x+12=0\) मिलता है। भिन्न हटाने के लिए पूरे समीकरण पर गुणा करें।
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Question 378/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किस समीकरण में (b=0) और (c>0) है?
Which equation has (b=0) and (c>0)?
#quadratic-equations
#coefficients
#missing-term
#medium
A \(x^2+6x+9=0\)
B \(5x^2+20=0\)
C \(2x^2-14=0\)
D \(x^2-x=0\)
Explanation opens after your attempt
Correct Answer
B. \(5x^2+20=0\)
Step 1
Concept
In \(5x^2+20=0\), the (x) term is absent, so (b=0) and (c=20>0). Treat a missing term coefficient as (0).
Step 2
Why this answer is correct
The correct answer is B. \(5x^2+20=0\). In \(5x^2+20=0\), the (x) term is absent, so (b=0) and (c=20>0). Treat a missing term coefficient as (0).
Step 3
Exam Tip
\(5x^2+20=0\) में (x) पद अनुपस्थित है, इसलिए (b=0) और (c=20>0) है। अनुपस्थित पद का गुणांक (0) मानें।
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Question 379/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(3x^2+10x+8=0\) में (ac) का मान क्या है?
What is the value of (ac) in \(3x^2+10x+8=0\)?
#quadratic-equations
#coefficients
#ac-product
#medium
A (24)
B (30)
C (18)
D (8)
Explanation opens after your attempt
Step 1
Concept
Here (a=3) and (c=8), so (ac=24). The value (ac) is useful in splitting the middle term.
Step 2
Why this answer is correct
The correct answer is A. (24). Here (a=3) and (c=8), so (ac=24). The value (ac) is useful in splitting the middle term.
Step 3
Exam Tip
यहाँ (a=3) और (c=8), इसलिए (ac=24) है। मध्य पद विभाजन में (ac) उपयोगी होता है।
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Question 380/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2+9x+20=0\) को गुणनखंड रूप में कौन-सा लिखा जा सकता है?
Which factor form can represent \(x^2+9x+20=0\)?
#quadratic-equations
#factor-form
#medium
A ((x+4)(x+5)=0)
B ((x-4)(x-5)=0)
C ((x+2)(x+10)=0)
D ((x-1)(x+20)=0)
Explanation opens after your attempt
Correct Answer
A. ((x+4)(x+5)=0)
Step 1
Concept
\(4\cdot5=20\) and (4+5=9). Therefore the correct factors are ((x+4)(x+5)).
Step 2
Why this answer is correct
The correct answer is A. ((x+4)(x+5)=0). \(4\cdot5=20\) and (4+5=9). Therefore the correct factors are ((x+4)(x+5)).
Step 3
Exam Tip
\(4\cdot5=20\) और (4+5=9) है। इसलिए सही गुणनखंड ((x+4)(x+5)) हैं।
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Question 381/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(16x^2-81=0\) के मूल क्या हैं?
What are the roots of \(16x^2-81=0\)?
#quadratic-equations
#roots
#difference-of-squares
#medium
A \(x=\pm \frac{9}{4}\)
B \(x=\pm \frac{4}{9}\)
C \(x=\pm 9\)
D \(x=\pm 4\)
Explanation opens after your attempt
Correct Answer
A. \(x=\pm \frac{9}{4}\)
Step 1
Concept
\(16x^2=81\), so \(x^2=\frac{81}{16}\) and \(x=\pm\frac{9}{4}\). Take both signs while taking square roots.
Step 2
Why this answer is correct
The correct answer is A. \(x=\pm \frac{9}{4}\). \(16x^2=81\), so \(x^2=\frac{81}{16}\) and \(x=\pm\frac{9}{4}\). Take both signs while taking square roots.
Step 3
Exam Tip
\(16x^2=81\), इसलिए \(x^2=\frac{81}{16}\) और \(x=\pm\frac{9}{4}\) है। वर्गमूल लेते समय दोनों चिन्ह लें।
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Question 382/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2+9x=0\) के मूल कौन-से हैं?
What are the roots of \(x^2+9x=0\)?
#quadratic-equations
#roots
#factorisation
#medium
A (0,-9)
B (0,9)
C (1,-9)
D (-1,9)
Explanation opens after your attempt
Step 1
Concept
(x-2 +9x=x(x+9)), so the roots are (0) and (-9). Taking the common factor is a quick method.
Step 2
Why this answer is correct
The correct answer is A. (0,-9). (x-2 +9x=x(x+9)), so the roots are (0) and (-9). Taking the common factor is a quick method.
Step 3
Exam Tip
(x-2 +9x=x(x+9)), इसलिए मूल (0) और (-9) हैं। समान गुणनखंड निकालना जल्दी तरीका है।
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Question 383/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
एक आयत की लंबाई चौड़ाई से (6) अधिक है और क्षेत्रफल (72) है। यदि चौड़ाई (x) है, तो समीकरण क्या होगा?
A rectangle has length (6) more than its breadth and area (72). If the breadth is (x), what is the equation?
#quadratic-equations
#area
#word-problem
#medium
A \(x^2+6x-72=0\)
B \(x^2-6x-72=0\)
C \(6x^2+x-72=0\)
D \(x^2+72x-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+6x-72=0\)
Step 1
Concept
The length is (x+6) and the area is (x(x+6)=72). Therefore \(x^2+6x-72=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+6x-72=0\). The length is (x+6) and the area is (x(x+6)=72). Therefore \(x^2+6x-72=0\).
Step 3
Exam Tip
लंबाई (x+6) होगी और क्षेत्रफल (x(x+6)=72) होगा। इसलिए \(x^2+6x-72=0\) है।
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Question 384/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
दो क्रमागत पूर्णांकों के वर्गों का योग (85) है। यदि छोटा पूर्णांक (x) है, तो समीकरण कौन-सा है?
The sum of squares of two consecutive integers is (85). If the smaller integer is (x), which equation is correct?
#quadratic-equations
#consecutive-integers
#word-problem
#medium
A \(2x^2+2x-84=0\)
B \(2x^2+2x-85=0\)
C \(x^2+x-85=0\)
D \(2x^2-x-85=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+2x-84=0\)
Step 1
Concept
The integers are (x) and (x+1), so (x-2 +(x+1)2 =85). Simplifying gives \(2x^2+2x-84=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+2x-84=0\). The integers are (x) and (x+1), so (x-2 +(x+1)2 =85). Simplifying gives \(2x^2+2x-84=0\).
Step 3
Exam Tip
पूर्णांक (x) और (x+1) होंगे, इसलिए (x-2 +(x+1)2 =85)। सरल करने पर \(2x^2+2x-84=0\) मिलता है।
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Question 385/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किसी संख्या (x) का वर्ग उसके (5) गुने से (24) अधिक है। सही समीकरण कौन-सा है?
The square of a number (x) is (24) more than (5) times it. Which equation is correct?
#quadratic-equations
#word-problem
#equation-formation
#medium
A \(x^2-5x-24=0\)
B \(x^2+5x-24=0\)
C \(x^2-24x-5=0\)
D \(5x^2-x-24=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-5x-24=0\)
Step 1
Concept
The statement gives \(x^2=5x+24\). Bringing all terms to one side gives \(x^2-5x-24=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-5x-24=0\). The statement gives \(x^2=5x+24\). Bringing all terms to one side gives \(x^2-5x-24=0\).
Step 3
Exam Tip
वाक्य से \(x^2=5x+24\) बनता है। सभी पद एक ओर लाने पर \(x^2-5x-24=0\) मिलता है।
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Question 386/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि मूल (-4) और (3) हैं, तो मोनिक द्विघात समीकरण कौन-सा होगा?
If the roots are (-4) and (3), what will be the monic quadratic equation?
#quadratic-equations
#monic
#roots
#medium
A \(x^2+x-12=0\)
B \(x^2-x-12=0\)
C \(x^2+7x+12=0\)
D \(x^2-7x+12=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x-12=0\)
Step 1
Concept
The factors will be ((x+4)) and ((x-3)). These give \(x^2+x-12=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x-12=0\). The factors will be ((x+4)) and ((x-3)). These give \(x^2+x-12=0\).
Step 3
Exam Tip
गुणनखंड ((x+4)) और ((x-3)) होंगे। इनसे \(x^2+x-12=0\) मिलता है।
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Question 387/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किस विकल्प में (x=2) और (x=7) मूल हैं?
Which option has roots (x=2) and (x=7)?
#quadratic-equations
#roots
#forming-equation
#medium
A \(x^2-9x+14=0\)
B \(x^2+9x+14=0\)
C \(x^2-14x+9=0\)
D \(x^2+14x-9=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-9x+14=0\)
Step 1
Concept
If the roots are (2) and (7), the factors are ((x-2)) and ((x-7)). Their product gives \(x^2-9x+14=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-9x+14=0\). If the roots are (2) and (7), the factors are ((x-2)) and ((x-7)). Their product gives \(x^2-9x+14=0\).
Step 3
Exam Tip
मूल (2) और (7) हों तो गुणनखंड ((x-2)) और ((x-7)) होंगे। इनका गुणन \(x^2-9x+14=0\) देता है।
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Question 388/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(3x^2+2x+7=0\) के विवेचक का चिन्ह क्या है?
What is the sign of the discriminant of \(3x^2+2x+7=0\)?
#quadratic-equations
#discriminant
#negative
#medium
A धनात्मक / Positive
B शून्य / Zero
C ऋणात्मक / Negative
D निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
C. ऋणात्मक / Negative
Step 1
Concept
\(D=2^2-4\cdot3\cdot7=4-84=-80\), so the discriminant is negative. Calculate (4ac) completely.
Step 2
Why this answer is correct
The correct answer is C. ऋणात्मक / Negative. \(D=2^2-4\cdot3\cdot7=4-84=-80\), so the discriminant is negative. Calculate (4ac) completely.
Step 3
Exam Tip
\(D=2^2-4\cdot3\cdot7=4-84=-80\), इसलिए विवेचक ऋणात्मक है। (4ac) की गणना पूरी करें।
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Question 389/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2-10x+25=0\) में मूलों की प्रकृति क्या है?
What is the nature of roots of \(x^2-10x+25=0\)?
#quadratic-equations
#nature-of-roots
#discriminant
#medium
A दो भिन्न वास्तविक मूल / Two distinct real roots
B दो समान वास्तविक मूल / Two equal real roots
C कोई वास्तविक मूल नहीं / No real roots
D तीन वास्तविक मूल / Three real roots
Explanation opens after your attempt
Correct Answer
B. दो समान वास्तविक मूल / Two equal real roots
Step 1
Concept
Here (D=(-10)2 -4\cdot1\cdot25=0), so the roots are equal. (D=0) identifies equal real roots.
Step 2
Why this answer is correct
The correct answer is B. दो समान वास्तविक मूल / Two equal real roots. Here (D=(-10)2 -4\cdot1\cdot25=0), so the roots are equal. (D=0) identifies equal real roots.
Step 3
Exam Tip
यहाँ (D=(-10)2 -4\cdot1\cdot25=0), इसलिए मूल समान हैं। (D=0) समान वास्तविक मूलों की पहचान है।
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Question 390/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि (D=49) है, तो द्विघात समीकरण के मूलों की प्रकृति क्या होगी?
If (D=49), what will be the nature of roots of the quadratic equation?
#quadratic-equations
#discriminant
#nature-of-roots
#medium
A दो भिन्न वास्तविक मूल / Two distinct real roots
B दो समान वास्तविक मूल / Two equal real roots
C कोई वास्तविक मूल नहीं / No real roots
D केवल एक मूल / Only one root
Explanation opens after your attempt
Correct Answer
A. दो भिन्न वास्तविक मूल / Two distinct real roots
Step 1
Concept
Since (D=49>0), two distinct real roots are obtained. The sign of the discriminant tells the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. दो भिन्न वास्तविक मूल / Two distinct real roots. Since (D=49>0), two distinct real roots are obtained. The sign of the discriminant tells the nature of roots.
Step 3
Exam Tip
(D=49>0), इसलिए दो भिन्न वास्तविक मूल मिलते हैं। विवेचक का चिन्ह मूलों की प्रकृति बताता है।
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