Question 1/12
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि \(x^2+bx+49=0\) की जड़ें समान और ऋणात्मक हैं, तो (b) का मान क्या होगा?
If \(x^2+bx+49=0\) has equal and negative roots, what is the value of (b)?
#quadratic-roots
#equal-negative-roots
#coefficient
A (-14)
B (14)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(b^2-196=0\), so \(b=\pm14\). The equal root \(-\frac{b}{2}\) must be negative, hence (b=14).
Step 2
Why this answer is correct
The correct answer is B. (14). For equal roots, \(b^2-196=0\), so \(b=\pm14\). The equal root \(-\frac{b}{2}\) must be negative, hence (b=14).
Step 3
Exam Tip
समान जड़ों के लिए \(b^2-196=0\), इसलिए \(b=\pm14\)। समान जड़ \(-\frac{b}{2}\) ऋणात्मक होनी चाहिए, अतः (b=14)।
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Question 2/12
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि \(x^2+bx+25=0\) की जड़ें समान और ऋणात्मक हैं, तो (b) का मान क्या होगा?
If \(x^2+bx+25=0\) has equal and negative roots, what is the value of (b)?
#quadratic-roots
#equal-negative-roots
#coefficient
A (10)
B (-10)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(b^2-100=0\), so \(b=\pm10\). The equal root \(-\frac{b}{2}\) must be negative, hence (b=10).
Step 2
Why this answer is correct
The correct answer is A. (10). For equal roots, \(b^2-100=0\), so \(b=\pm10\). The equal root \(-\frac{b}{2}\) must be negative, hence (b=10).
Step 3
Exam Tip
समान जड़ों के लिए \(b^2-100=0\), इसलिए \(b=\pm10\)। समान जड़ \(-\frac{b}{2}\) ऋणात्मक होनी चाहिए, अतः (b=10)।
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Question 3/12
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
\(2x^2+kx+2=0\) की जड़ें समान और ऋणात्मक हों, तो (k) का मान क्या होगा?
If \(2x^2+kx+2=0\) has equal and negative roots, what is (k)?
#quadratic-roots
#equal-negative-roots
#parameter
A (4)
B (-4)
C (2)
D (-2)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(k^2-16=0\), so \(k=\pm4\). The equal root is \(-\frac{k}{4}\), which is negative only when (k=4).
Step 2
Why this answer is correct
The correct answer is A. (4). For equal roots, \(k^2-16=0\), so \(k=\pm4\). The equal root is \(-\frac{k}{4}\), which is negative only when (k=4).
Step 3
Exam Tip
समान जड़ों के लिए \(k^2-16=0\), इसलिए \(k=\pm4\)। समान जड़ \(-\frac{k}{4}\) है, जो ऋणात्मक तभी होगी जब (k=4)।
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Question 4/12
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि \(x^2+kx+49=0\) के मूल एक दूसरे के बराबर और ऋणात्मक हैं तो (k) क्या होगा?
If roots of \(x^2+kx+49=0\) are equal and negative, what is (k)?
#roots
#equal_negative_roots
#parameter
A (14)
B (-14)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The equal negative roots are (-7) and (-7). Their sum is (-14), so (k=14).
Step 2
Why this answer is correct
The correct answer is A. (14). The equal negative roots are (-7) and (-7). Their sum is (-14), so (k=14).
Step 3
Exam Tip
बराबर ऋणात्मक मूल (-7) और (-7) हैं। योग (-14) है इसलिए (k=14) है।
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Question 5/12
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि समीकरण \(x^2+px+25=0\) के मूल बराबर हैं और दोनों ऋणात्मक हैं तो (p) का मान क्या होगा?
If the roots of \(x^2+px+25=0\) are equal and both negative, what is the value of (p)?
#roots
#equal_negative_roots
#parameter
A (10)
B (-10)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
The equal negative roots are (-5) and (-5) because the product is (25). The sum is (-10), so (p=10).
Step 2
Why this answer is correct
The correct answer is A. (10). The equal negative roots are (-5) and (-5) because the product is (25). The sum is (-10), so (p=10).
Step 3
Exam Tip
बराबर ऋणात्मक मूल (-5) और (-5) होंगे क्योंकि गुणनफल (25) है। योग (-10) है इसलिए (p=10) है।
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Question 6/12
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि \(x^2+kx+36=0\) के मूल एक दूसरे के बराबर और ऋणात्मक हैं तो (k) क्या होगा?
If roots of \(x^2+kx+36=0\) are equal and negative, what is (k)?
#roots
#equal_negative_roots
#parameter
A (12)
B (-12)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The equal negative roots are (-6) and (-6). Their sum is (-12), so (-k=-12) gives (k=12).
Step 2
Why this answer is correct
The correct answer is A. (12). The equal negative roots are (-6) and (-6). Their sum is (-12), so (-k=-12) gives (k=12).
Step 3
Exam Tip
बराबर ऋणात्मक मूल (-6) और (-6) हैं। योग (-12) है इसलिए (-k=-12) से (k=12) है।
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Question 7/12
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि समीकरण \(x^2+px+16=0\) के मूल बराबर हैं और दोनों ऋणात्मक हैं तो (p) का मान क्या होगा?
If the roots of \(x^2+px+16=0\) are equal and both negative, what is the value of (p)?
#roots
#equal_negative_roots
#parameter
A (8)
B (-8)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
For equal roots, the roots are (-4) and (-4) because the product is (16). The sum is (-8), so (-p=-8) gives (p=8).
Step 2
Why this answer is correct
The correct answer is A. (8). For equal roots, the roots are (-4) and (-4) because the product is (16). The sum is (-8), so (-p=-8) gives (p=8).
Step 3
Exam Tip
बराबर मूलों के लिए मूल (-4) और (-4) होंगे क्योंकि गुणनफल (16) है। योग (-8) है इसलिए (-p=-8) से (p=8) है।
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Question 8/12
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 9/12
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
किस समीकरण में मूल बराबर और ऋणात्मक होंगे?
Which equation will have equal and negative roots?
#quadratic-equations
#equal-negative-roots
#perfect-square
#hard
A \(x^2+16x+64=0\)
B \(x^2-16x+64=0\)
C \(x^2-64=0\)
D \(x^2+64=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+16x+64=0\)
Step 1
Concept
(x-2 +16x+64=(x+8)2 ), so both roots are (-8). Both roots are equal and negative.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+16x+64=0\). (x-2 +16x+64=(x+8)2 ), so both roots are (-8). Both roots are equal and negative.
Step 3
Exam Tip
(x-2 +16x+64=(x+8)2 ), इसलिए दोनों मूल (-8) हैं। दोनों मूल बराबर और ऋणात्मक हैं।
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Question 10/12
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2+px+9=0\) के मूल समान और ऋणात्मक हैं। (p) का मान क्या होगा?
The roots of \(x^2+px+9=0\) are equal and negative. What is the value of (p)?
#quadratic-equations
#equal-negative-roots
#parameter
#hard
A (6)
B (-6)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(p^2-36=0\) gives \(p=\pm6\). For equal negative roots, \(-\frac{p}{2}<0\), so (p=6).
Step 2
Why this answer is correct
The correct answer is A. (6). For equal roots, \(p^2-36=0\) gives \(p=\pm6\). For equal negative roots, \(-\frac{p}{2}<0\), so (p=6).
Step 3
Exam Tip
समान मूलों के लिए \(p^2-36=0\) से \(p=\pm6\) मिलता है। ऋणात्मक समान मूल के लिए \(-\frac{p}{2}<0\), इसलिए (p=6)।
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Question 11/12
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2+kx+81=0\) में यदि मूल समान और ऋणात्मक हैं, तो (k) का संभव मान कौन-सा है?
In \(x^2+kx+81=0\), if the roots are equal and negative, which possible value of (k) is correct?
#quadratic-equations
#equal-negative-roots
#parameter
#medium
A (18)
B (-18)
C (9)
D (-9)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(k^2=324\), and the equal root is \(-\frac{k}{2}\). For a negative root, (k=18) is correct.
Step 2
Why this answer is correct
The correct answer is A. (18). For equal roots, \(k^2=324\), and the equal root is \(-\frac{k}{2}\). For a negative root, (k=18) is correct.
Step 3
Exam Tip
समान मूलों के लिए \(k^2=324\) और समान मूल \(-\frac{k}{2}\) होगा। ऋणात्मक मूल के लिए (k=18) सही है।
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Question 12/12
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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