समीकरण \(x^2-10x+k=0\) के बराबर वास्तविक मूल होने के लिए (k) का मान क्या होगा?
For \(x^2-10x+k=0\) to have equal real roots, what should be the value of (k)?
#roots
#equal_roots
#parameter
A (25)
B (10)
C (5)
D (100)
Explanation opens after your attempt
Step 1
Concept
For equal roots (D=0). From (100-4k=0), we get (k=25).
Step 2
Why this answer is correct
The correct answer is A. (25). For equal roots (D=0). From (100-4k=0), we get (k=25).
Step 3
Exam Tip
बराबर मूलों के लिए (D=0) होता है। (100-4k=0) से (k=25) मिलता है।
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समीकरण \(4x^2-20x+25=0\) का डिस्क्रिमिनेंट (D) क्या है?
What is the discriminant (D) of \(4x^2-20x+25=0\)?
#roots
#discriminant
#equal_roots
A (0)
B (20)
C (-20)
D (100)
Explanation opens after your attempt
Step 1
Concept
Here \(D=b^2-4ac=400-400=0\). Therefore its two real roots will be equal.
Step 2
Why this answer is correct
The correct answer is A. (0). Here \(D=b^2-4ac=400-400=0\). Therefore its two real roots will be equal.
Step 3
Exam Tip
यहां \(D=b^2-4ac=400-400=0\) है। इसलिए इसके दोनों वास्तविक मूल बराबर होंगे।
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यदि \(x^2+ax+16=0\) के मूल (4) और (4) हैं तो (a) का मान क्या है?
If the roots of \(x^2+ax+16=0\) are (4) and (4), what is the value of (a)?
#roots
#parameter
#equal_roots
A (-8)
B (8)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (8), and (-a=8). Therefore (a=-8).
Step 2
Why this answer is correct
The correct answer is A. (-8). The sum of roots is (8), and (-a=8). Therefore (a=-8).
Step 3
Exam Tip
मूलों का योग (8) है और (-a=8) होगा। इसलिए (a=-8) है।
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यदि (D=0) और मूलों का योग (12) है तो प्रत्येक मूल क्या होगा?
If (D=0) and the sum of roots is (12), what will each root be?
#roots
#equal_roots
#sum
A (6)
B (12)
C (0)
D (24)
Explanation opens after your attempt
Step 1
Concept
When (D=0), both roots are equal. Therefore each root is \(\frac{12}{2}=6\).
Step 2
Why this answer is correct
The correct answer is A. (6). When (D=0), both roots are equal. Therefore each root is \(\frac{12}{2}=6\).
Step 3
Exam Tip
(D=0) होने पर दोनों मूल बराबर होते हैं। इसलिए प्रत्येक मूल \(\frac{12}{2}=6\) होगा।
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समीकरण \(x^2+px+25=0\) के दोनों मूल (-5) और (-5) हैं तो (p) का मान क्या है?
If both roots of \(x^2+px+25=0\) are (-5) and (-5), what is the value of (p)?
#roots
#equal_roots
#parameter
A (10)
B (-10)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (-10), and (-p=-10). Therefore (p=10).
Step 2
Why this answer is correct
The correct answer is A. (10). The sum of roots is (-10), and (-p=-10). Therefore (p=10).
Step 3
Exam Tip
मूलों का योग (-10) है और (-p=-10) होगा। इसलिए (p=10) है।
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समीकरण \(x^2-8x+k=0\) के बराबर वास्तविक मूल होने के लिए (k) का मान क्या होगा?
For \(x^2-8x+k=0\) to have equal real roots, what should be the value of (k)?
#roots
#equal_roots
#parameter
A (16)
B (8)
C (4)
D (64)
Explanation opens after your attempt
Step 1
Concept
For equal roots (D=0). From (64-4k=0), we get (k=16).
Step 2
Why this answer is correct
The correct answer is A. (16). For equal roots (D=0). From (64-4k=0), we get (k=16).
Step 3
Exam Tip
बराबर मूलों के लिए (D=0) होता है। (64-4k=0) से (k=16) मिलता है।
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समीकरण \(3x^2-6x+3=0\) का डिस्क्रिमिनेंट (D) क्या है?
What is the discriminant (D) of \(3x^2-6x+3=0\)?
#roots
#discriminant
#equal_roots
A (0)
B (6)
C (-6)
D (12)
Explanation opens after your attempt
Step 1
Concept
Here \(D=b^2-4ac=36-36=0\). Therefore the two real roots will be equal.
Step 2
Why this answer is correct
The correct answer is A. (0). Here \(D=b^2-4ac=36-36=0\). Therefore the two real roots will be equal.
Step 3
Exam Tip
यहां \(D=b^2-4ac=36-36=0\) है। इसलिए दोनों वास्तविक मूल बराबर होंगे।
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यदि \(x^2+ax+9=0\) के मूल (3) और (3) हैं तो (a) का मान क्या है?
If the roots of \(x^2+ax+9=0\) are (3) and (3), what is the value of (a)?
#roots
#parameter
#equal_roots
A (-6)
B (6)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (6), and (-a=6). Therefore (a=-6).
Step 2
Why this answer is correct
The correct answer is A. (-6). The sum of roots is (6), and (-a=6). Therefore (a=-6).
Step 3
Exam Tip
मूलों का योग (6) है और (-a=6) होगा। इसलिए (a=-6) है।
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यदि (D=0) और मूलों का योग (10) है तो प्रत्येक मूल क्या होगा?
If (D=0) and the sum of roots is (10), what will each root be?
#roots
#equal_roots
#sum
A (5)
B (10)
C (0)
D (20)
Explanation opens after your attempt
Step 1
Concept
When (D=0), both roots are equal. Therefore each root is \(\frac{10}{2}=5\).
Step 2
Why this answer is correct
The correct answer is A. (5). When (D=0), both roots are equal. Therefore each root is \(\frac{10}{2}=5\).
Step 3
Exam Tip
(D=0) होने पर दोनों मूल बराबर होते हैं। इसलिए प्रत्येक मूल \(\frac{10}{2}=5\) होगा।
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समीकरण \(x^2+px+16=0\) के दोनों मूल (-4) और (-4) हैं तो (p) का मान क्या है?
If both roots of \(x^2+px+16=0\) are (-4) and (-4), what is the value of (p)?
#roots
#equal_roots
#parameter
A (8)
B (-8)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (-8), and (-p=-8). Therefore (p=8).
Step 2
Why this answer is correct
The correct answer is A. (8). The sum of roots is (-8), and (-p=-8). Therefore (p=8).
Step 3
Exam Tip
मूलों का योग (-8) है और (-p=-8) होगा। इसलिए (p=8) है।
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समीकरण \(x^2-6x+k=0\) के बराबर वास्तविक मूल होने के लिए (k) का मान क्या होगा?
For \(x^2-6x+k=0\) to have equal real roots, what should be the value of (k)?
#roots
#equal_roots
#parameter
A (9)
B (6)
C (3)
D (36)
Explanation opens after your attempt
Step 1
Concept
For equal roots (D=0). From (36-4k=0), we get (k=9).
Step 2
Why this answer is correct
The correct answer is A. (9). For equal roots (D=0). From (36-4k=0), we get (k=9).
Step 3
Exam Tip
बराबर मूलों के लिए (D=0) होता है। (36-4k=0) से (k=9) मिलता है।
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समीकरण \(2x^2-4x+2=0\) का डिस्क्रिमिनेंट (D) क्या है?
What is the discriminant (D) of \(2x^2-4x+2=0\)?
#roots
#discriminant
#equal_roots
A (0)
B (4)
C (-4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Here \(D=b^2-4ac=16-16=0\). Therefore the two real roots will be equal.
Step 2
Why this answer is correct
The correct answer is A. (0). Here \(D=b^2-4ac=16-16=0\). Therefore the two real roots will be equal.
Step 3
Exam Tip
यहां \(D=b^2-4ac=16-16=0\) है। इसलिए दोनों वास्तविक मूल बराबर होंगे।
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यदि किसी मोनिक द्विघात समीकरण के दोनों मूल (5) और (5) हैं तो समीकरण कौन सा है?
If both roots of a monic quadratic equation are (5) and (5), which equation is it?
#roots
#equal_roots
#equation_from_roots
A \(x^2-10x+25=0\)
B \(x^2+10x+25=0\)
C \(x^2-5x+25=0\)
D \(x^2+5x-25=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-10x+25=0\)
Step 1
Concept
If both roots are (5), the equation is ((x-5)2 =0). Expanding it gives \(x^2-10x+25=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-10x+25=0\). If both roots are (5), the equation is ((x-5)2 =0). Expanding it gives \(x^2-10x+25=0\).
Step 3
Exam Tip
दोनों मूल (5) हों तो समीकरण ((x-5)2 =0) होगा। इसे खोलने पर \(x^2-10x+25=0\) मिलता है।
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यदि किसी द्विघात समीकरण के मूल (r) और (r) हैं तो उनके गुणनफल का मान क्या होगा?
If the roots of a quadratic equation are (r) and (r), what will be their product?
#roots
#equal_roots
#product
A (2r)
B (0)
C \(r^2\)
D (r)
Explanation opens after your attempt
Correct Answer
C. \(r^2\)
Step 1
Concept
The product of (r) and (r) is \(r^2\). For equal roots, remember sum (2r) and product \(r^2\).
Step 2
Why this answer is correct
The correct answer is C. \(r^2\). The product of (r) and (r) is \(r^2\). For equal roots, remember sum (2r) and product \(r^2\).
Step 3
Exam Tip
(r) और (r) का गुणनफल \(r^2\) होता है। बराबर मूलों में योग (2r) और गुणनफल \(r^2\) याद रखें।
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यदि (D=0) है तो द्विघात समीकरण के वास्तविक मूल कैसे होते हैं?
If (D=0), how are the real roots of a quadratic equation?
#roots
#discriminant
#equal_roots
A दो भिन्न वास्तविक मूल / Two distinct real roots
B दो बराबर वास्तविक मूल / Two equal real roots
C कोई वास्तविक मूल नहीं / No real root
D चार वास्तविक मूल / Four real roots
Explanation opens after your attempt
Correct Answer
B. दो बराबर वास्तविक मूल / Two equal real roots
Step 1
Concept
When (D=0), the two real roots are equal. Check \(D=b^2-4ac\) for the nature of roots.
Step 2
Why this answer is correct
The correct answer is B. दो बराबर वास्तविक मूल / Two equal real roots. When (D=0), the two real roots are equal. Check \(D=b^2-4ac\) for the nature of roots.
Step 3
Exam Tip
(D=0) होने पर दोनों वास्तविक मूल बराबर होते हैं। मूलों की प्रकृति के लिए \(D=b^2-4ac\) देखें।
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यदि किसी मोनिक द्विघात समीकरण के दोनों मूल (-4) और (-4) हैं तो समीकरण कौन सा है?
If both roots of a monic quadratic equation are (-4) and (-4), which equation is it?
#roots
#equal_roots
#equation_from_roots
A \(x^2+8x+16=0\)
B \(x^2-8x+16=0\)
C \(x^2+4x+16=0\)
D \(x^2-4x-16=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+8x+16=0\)
Step 1
Concept
If both roots are (-4), the equation is ((x+4)2 =0). Expanding it gives \(x^2+8x+16=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+8x+16=0\). If both roots are (-4), the equation is ((x+4)2 =0). Expanding it gives \(x^2+8x+16=0\).
Step 3
Exam Tip
दोनों मूल (-4) हों तो समीकरण ((x+4)2 =0) होगा। इसे खोलने पर \(x^2+8x+16=0\) मिलता है।
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यदि किसी मोनिक द्विघात समीकरण के दोनों मूल (7) और (7) हैं तो समीकरण कौन सा है?
If both roots of a monic quadratic equation are (7) and (7) then which equation is it?
#roots
#equal_roots
#equation_from_roots
A \(x^2-14x+49=0\)
B \(x^2+14x+49=0\)
C \(x^2-7x+49=0\)
D \(x^2+7x-49=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-14x+49=0\)
Step 1
Concept
With both roots (7) we get ((x-7)2 =0) which is \(x^2-14x+49=0\). Form a perfect square from repeated roots.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-14x+49=0\). With both roots (7) we get ((x-7)2 =0) which is \(x^2-14x+49=0\). Form a perfect square from repeated roots.
Step 3
Exam Tip
दोनों मूल (7) होने पर ((x-7)2 =0) मिलता है जो \(x^2-14x+49=0\) है। दोहराए मूल से पूर्ण वर्ग बनाएं।
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यदि किसी द्विघात समीकरण के दो बराबर वास्तविक मूल हों तो डिस्क्रिमिनेंट (D) का मान कैसा होता है?
If a quadratic equation has two equal real roots then what is the value of discriminant (D)?
#roots
#discriminant
#equal_roots
A (D>0)
B (D=0)
C (D<0)
D (D=1)
Explanation opens after your attempt
Step 1
Concept
For equal real roots (D=0). The discriminant quickly tells the nature of roots.
Step 2
Why this answer is correct
The correct answer is B. (D=0). For equal real roots (D=0). The discriminant quickly tells the nature of roots.
Step 3
Exam Tip
बराबर वास्तविक मूलों के लिए (D=0) होता है। डिस्क्रिमिनेंट से मूलों की प्रकृति जल्दी पता चलती है।
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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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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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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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यदि \(x^2-2mx+49=0\) के मूल समान हैं, तो (m) के संभावित मान क्या हैं?
If the roots of \(x^2-2mx+49=0\) are equal, what are the possible values of (m)?
#quadratic-equations
#equal-roots
#discriminant
#expert
A \(m=\pm7\)
B \(m=\pm14\)
C (m=7)
D (m=-7)
Explanation opens after your attempt
Correct Answer
A. \(m=\pm7\)
Step 1
Concept
For equal roots, (D=0) is needed. Here ((-2m)2 -196=0), so \(m=\pm7\).
Step 2
Why this answer is correct
The correct answer is A. \(m=\pm7\). For equal roots, (D=0) is needed. Here ((-2m)2 -196=0), so \(m=\pm7\).
Step 3
Exam Tip
समान मूलों के लिए (D=0) चाहिए। यहाँ ((-2m)2 -196=0), इसलिए \(m=\pm7\)।
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यदि समीकरण \(x^2+bx+64=0\) के दोनों मूल समान हैं और उनका मान (-8) है, तो (b) क्या है?
If both roots of \(x^2+bx+64=0\) are equal and their value is (-8), what is (b)?
#quadratic-equations
#equal-roots
#coefficient
#expert
A (16)
B (-16)
C (8)
D (-8)
Explanation opens after your attempt
Step 1
Concept
Both roots are (-8), so the sum is (-16). Here the sum of roots is (-b), so (b=16).
Step 2
Why this answer is correct
The correct answer is A. (16). Both roots are (-8), so the sum is (-16). Here the sum of roots is (-b), so (b=16).
Step 3
Exam Tip
दोनों मूल (-8) हैं, इसलिए योग (-16) है। यहाँ मूलों का योग (-b) है, अतः (b=16)।
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यदि \(x^2-2mx+36=0\) के मूल समान हैं, तो (m) के संभावित मान क्या हैं?
If the roots of \(x^2-2mx+36=0\) are equal, what are the possible values of (m)?
#quadratic-equations
#equal-roots
#discriminant
#expert
A \(m=\pm6\)
B \(m=\pm12\)
C (m=6)
D (m=-6)
Explanation opens after your attempt
Correct Answer
A. \(m=\pm6\)
Step 1
Concept
For equal roots, (D=0), so ((-2m)2 -144=0). This gives \(m^2=36\) and \(m=\pm6\).
Step 2
Why this answer is correct
The correct answer is A. \(m=\pm6\). For equal roots, (D=0), so ((-2m)2 -144=0). This gives \(m^2=36\) and \(m=\pm6\).
Step 3
Exam Tip
समान मूलों के लिए (D=0), अतः ((-2m)2 -144=0) होगा। इससे \(m^2=36\) और \(m=\pm6\) है।
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यदि समीकरण \(x^2+bx+49=0\) के दोनों मूल समान हैं और उनका मान (-7) है, तो (b) क्या है?
If both roots of \(x^2+bx+49=0\) are equal and their value is (-7), what is (b)?
#quadratic-equations
#equal-roots
#coefficient
#hard
A (14)
B (-14)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
Both roots are (-7), so their sum is (-14). Here the sum of roots is (-b), so (b=14).
Step 2
Why this answer is correct
The correct answer is A. (14). Both roots are (-7), so their sum is (-14). Here the sum of roots is (-b), so (b=14).
Step 3
Exam Tip
दोनों मूल (-7) हैं, इसलिए योग (-14) है। यहाँ मूलों का योग (-b) है, अतः (b=14)।
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यदि \(x^2-2kx+25=0\) के मूल समान हैं, तो (k) के संभावित मान क्या हैं?
If the roots of \(x^2-2kx+25=0\) are equal, what are the possible values of (k)?
#quadratic-equations
#equal-roots
#discriminant
#hard
A \(k=\pm5\)
B \(k=\pm10\)
C (k=5)
D (k=-5)
Explanation opens after your attempt
Correct Answer
A. \(k=\pm5\)
Step 1
Concept
For equal roots, (D=0), so ((-2k)2 -100=0). This gives \(k^2=25\) and \(k=\pm5\).
Step 2
Why this answer is correct
The correct answer is A. \(k=\pm5\). For equal roots, (D=0), so ((-2k)2 -100=0). This gives \(k^2=25\) and \(k=\pm5\).
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए ((-2k)2 -100=0) मिलता है। इससे \(k^2=25\) और \(k=\pm5\) है।
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यदि समीकरण \(x^2+bx+25=0\) के दोनों मूल समान हैं और उनका मान (-5) है, तो (b) क्या है?
If both roots of \(x^2+bx+25=0\) are equal and their value is (-5), what is (b)?
#quadratic-equations
#equal-roots
#coefficient
#hard
A (10)
B (-10)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
Both roots are (-5), so their sum is (-10). Here the sum of roots is (-b), so (b=10).
Step 2
Why this answer is correct
The correct answer is A. (10). Both roots are (-5), so their sum is (-10). Here the sum of roots is (-b), so (b=10).
Step 3
Exam Tip
दोनों मूल (-5) हैं, इसलिए योग (-10) है। यहाँ मूलों का योग (-b) है, अतः (b=10)।
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यदि \(x^2-2kx+16=0\) के मूल समान हैं, तो (k) के संभावित मान क्या हैं?
If the roots of \(x^2-2kx+16=0\) are equal, what are the possible values of (k)?
#quadratic-equations
#equal-roots
#discriminant
#hard
A \(k=\pm4\)
B \(k=\pm8\)
C (k=4)
D (k=-4)
Explanation opens after your attempt
Correct Answer
A. \(k=\pm4\)
Step 1
Concept
For equal roots, (D=0), so ((-2k)2 -64=0). This gives \(k^2=16\) and \(k=\pm4\).
Step 2
Why this answer is correct
The correct answer is A. \(k=\pm4\). For equal roots, (D=0), so ((-2k)2 -64=0). This gives \(k^2=16\) and \(k=\pm4\).
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए ((-2k)2 -64=0) मिलता है। इससे \(k^2=16\) और \(k=\pm4\) है।
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यदि द्विघात समीकरण \(x^2-18x+k=0\) के मूल समान हैं, तो (k) क्या होगा?
If the roots of \(x^2-18x+k=0\) are equal, what is (k)?
#quadratic-equations
#equal-roots
#discriminant
#medium
A (18)
B (81)
C (162)
D (324)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (324-4k=0) and (k=81). For equal roots, set the discriminant to zero.
Step 2
Why this answer is correct
The correct answer is B. (81). For equal roots, (D=0), so (324-4k=0) and (k=81). For equal roots, set the discriminant to zero.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (324-4k=0) और (k=81)। समान मूल की शर्त में विवेचक शून्य रखें।
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यदि \(x^2+ux+64=0\) के मूल (8) और (8) हैं, तो (u) का मान क्या होगा?
If the roots of \(x^2+ux+64=0\) are (8) and (8), what is the value of (u)?
#quadratic-equations
#equal-roots
#parameter
#medium
A (16)
B (-16)
C (8)
D (-8)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (16), and in \(x^2+ux+64=0\), the sum is (-u). Therefore (u=-16).
Step 2
Why this answer is correct
The correct answer is B. (-16). The sum of roots is (16), and in \(x^2+ux+64=0\), the sum is (-u). Therefore (u=-16).
Step 3
Exam Tip
मूलों का योग (16) है और \(x^2+ux+64=0\) में योग (-u) होता है। इसलिए (u=-16) है।
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