यदि (2) समीकरण \(x^2+kx-14=0\) का मूल है तो (k) का मान क्या होगा?
If (2) is a root of \(x^2+kx-14=0\), what is the value of (k)?
#roots
#parameter
#substitution
A (5)
B (-5)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
Putting (x=2) gives (4+2k-14=0), so (k=5). In parameter questions substitute the given root directly.
Step 2
Why this answer is correct
The correct answer is A. (5). Putting (x=2) gives (4+2k-14=0), so (k=5). In parameter questions substitute the given root directly.
Step 3
Exam Tip
(x=2) रखने पर (4+2k-14=0) इसलिए (k=5) है। पैरामीटर के प्रश्न में दिए मूल को सीधे रखें।
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क्या (x=3) समीकरण \(x^2-7x+12=0\) का मूल है?
Is (x=3) a root of \(x^2-7x+12=0\)?
#roots
#checking
#substitution
A हाँ / Yes
B नहीं / No
C केवल (x=4) मूल है / Only (x=4) is a root
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=3) gives (9-21+12=0). Therefore (3) is a root of this equation.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=3) gives (9-21+12=0). Therefore (3) is a root of this equation.
Step 3
Exam Tip
(x=3) रखने पर (9-21+12=0) मिलता है। इसलिए (3) इस समीकरण का मूल है।
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यदि किसी द्विघात बहुपद (p(x)) के लिए (p(r)=0) है तो (r) के बारे में सही कथन कौन सा है?
If (p(r)=0) for a quadratic polynomial (p(x)), which statement about (r) is correct?
#roots
#definition
#substitution
A (r) समीकरण (p(x)=0) का मूल है / (r) is a root of (p(x)=0)
B (r) केवल (p(x)) का गुणांक है / (r) is only a coefficient of (p(x))
C (r) हमेशा अचर पद है / (r) is always the constant term
D (r) हमेशा शून्य नहीं हो सकता / (r) can never be zero
Explanation opens after your attempt
Correct Answer
A. (r) समीकरण (p(x)=0) का मूल है / (r) is a root of (p(x)=0)
Step 1
Concept
(p(r)=0) means the equation is satisfied when (x=r). Substitution is the safest way to check a root.
Step 2
Why this answer is correct
The correct answer is A. (r) समीकरण (p(x)=0) का मूल है / (r) is a root of (p(x)=0). (p(r)=0) means the equation is satisfied when (x=r). Substitution is the safest way to check a root.
Step 3
Exam Tip
(p(r)=0) का अर्थ है कि (x=r) रखने पर समीकरण संतुष्ट होता है। मूल जांचने के लिए प्रतिस्थापन सबसे सुरक्षित तरीका है।
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यदि (4) समीकरण \(2x^2-9x+n=0\) का मूल है तो (n) का मान क्या है?
If (4) is a root of \(2x^2-9x+n=0\), what is the value of (n)?
#roots
#parameter
#substitution
A (2)
B (4)
C (-4)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Putting (x=4) gives (32-36+n=0), so (n=4). Calculate each term separately.
Step 2
Why this answer is correct
The correct answer is B. (4). Putting (x=4) gives (32-36+n=0), so (n=4). Calculate each term separately.
Step 3
Exam Tip
(x=4) रखने पर (32-36+n=0) इसलिए (n=4)। गणना में हर पद अलग अलग निकालें।
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यदि (3) समीकरण \(x^2+sx-12=0\) का मूल है तो (s) का मान क्या है?
If (3) is a root of \(x^2+sx-12=0\), what is the value of (s)?
#roots
#parameter
#substitution
A (1)
B (-1)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
Putting (x=3) gives (9+3s-12=0), so (s=1). Substitute the given root directly into the equation.
Step 2
Why this answer is correct
The correct answer is A. (1). Putting (x=3) gives (9+3s-12=0), so (s=1). Substitute the given root directly into the equation.
Step 3
Exam Tip
(x=3) रखने पर (9+3s-12=0) इसलिए (s=1)। दिए गए मूल को सीधे समीकरण में रखें।
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क्या (x=2) समीकरण \(x^2-4x+4=0\) का मूल है?
Is (x=2) a root of \(x^2-4x+4=0\)?
#roots
#checking
#substitution
A हाँ / Yes
B नहीं / No
C केवल (x=4) पर / Only at (x=4)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=2) gives (4-8+4=0). Therefore (2) is a root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=2) gives (4-8+4=0). Therefore (2) is a root.
Step 3
Exam Tip
(x=2) रखने पर (4-8+4=0) मिलता है। इसलिए (2) इसका मूल है।
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यदि (2) समीकरण \(3x^2-8x+n=0\) का मूल है तो (n) का मान क्या है?
If (2) is a root of \(3x^2-8x+n=0\), what is the value of (n)?
#roots
#parameter
#substitution
A (2)
B (4)
C (-4)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Putting (x=2) gives (12-16+n=0), so (n=4). In such questions calculate slowly and correctly.
Step 2
Why this answer is correct
The correct answer is B. (4). Putting (x=2) gives (12-16+n=0), so (n=4). In such questions calculate slowly and correctly.
Step 3
Exam Tip
(x=2) रखने पर (12-16+n=0) इसलिए (n=4)। ऐसे प्रश्नों में गणना धीरे और सही करें।
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यदि (2) समीकरण \(x^2+qx-10=0\) का मूल है तो (q) का मान क्या है?
If (2) is a root of \(x^2+qx-10=0\), what is the value of (q)?
#roots
#parameter
#substitution
A (2)
B (3)
C (-3)
D (5)
Explanation opens after your attempt
Step 1
Concept
Putting (x=2) gives (4+2q-10=0), so (q=3). Substitute the given root directly into the equation.
Step 2
Why this answer is correct
The correct answer is B. (3). Putting (x=2) gives (4+2q-10=0), so (q=3). Substitute the given root directly into the equation.
Step 3
Exam Tip
(x=2) रखने पर (4+2q-10=0) इसलिए (q=3)। दिए गए मूल को सीधे समीकरण में रखें।
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क्या (x=1) समीकरण \(x^2-3x+2=0\) का मूल है?
Is (x=1) a root of \(x^2-3x+2=0\)?
#roots
#checking
#substitution
A हाँ / Yes
B नहीं / No
C केवल (x=2) पर / Only at (x=2)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=1) gives (1-3+2=0). Therefore (1) is a root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=1) gives (1-3+2=0). Therefore (1) is a root.
Step 3
Exam Tip
(x=1) रखने पर (1-3+2=0) मिलता है। इसलिए (1) इसका मूल है।
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यदि (x=3) समीकरण \(2x^2-7x+k=0\) का मूल है तो (k) का मान क्या होगा?
If (x=3) is a root of \(2x^2-7x+k=0\), what will be the value of (k)?
#roots
#parameter
#substitution
A (3)
B (6)
C (-3)
D (-6)
Explanation opens after your attempt
Step 1
Concept
Putting (x=3) gives (18-21+k=0), so (k=3). In such questions substitute the given root directly into the equation.
Step 2
Why this answer is correct
The correct answer is A. (3). Putting (x=3) gives (18-21+k=0), so (k=3). In such questions substitute the given root directly into the equation.
Step 3
Exam Tip
(x=3) रखने पर (18-21+k=0) इसलिए (k=3) मिलता है। ऐसे प्रश्नों में दिए हुए मूल को सीधे समीकरण में रखें।
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यदि (1) समीकरण \(2x^2-3x+m=0\) का मूल है तो (m) का मान क्या है?
If (1) is a root of \(2x^2-3x+m=0\) then what is the value of (m)?
#roots
#parameter
#substitution
A (-1)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
Putting (x=1) gives (2-3+m=0) so (m=1). When a root is given substitute directly in the equation.
Step 2
Why this answer is correct
The correct answer is B. (1). Putting (x=1) gives (2-3+m=0) so (m=1). When a root is given substitute directly in the equation.
Step 3
Exam Tip
(x=1) रखने पर (2-3+m=0) इसलिए (m=1)। मूल दिया हो तो समीकरण में सीधा प्रतिस्थापन करें।
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यदि (1) समीकरण \(x^2-kx+2=0\) का मूल है तो (k) का मान क्या है?
If (1) is a root of \(x^2-kx+2=0\) then what is the value of (k)?
#roots
#parameter
#substitution
A (3)
B (2)
C (1)
D (-3)
Explanation opens after your attempt
Step 1
Concept
Putting (x=1) gives (1-k+2=0) so (k=3). Substitute the given root directly in the equation.
Step 2
Why this answer is correct
The correct answer is A. (3). Putting (x=1) gives (1-k+2=0) so (k=3). Substitute the given root directly in the equation.
Step 3
Exam Tip
(x=1) रखने पर (1-k+2=0) इसलिए (k=3) है। दिए गए मूल को सीधे समीकरण में रखें।
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यदि (p(2)=0) है तो (2) के बारे में सही कथन कौन सा है?
If (p(2)=0) then which statement about (2) is correct?
#roots
#substitution
#concept
A (2) (p(x)=0) का मूल है / (2) is a root of (p(x)=0)
B (2) गुणांक है / (2) is a coefficient
C (2) अचर पद है / (2) is a constant term
D (2) घात है / (2) is the degree
Explanation opens after your attempt
Correct Answer
A. (2) (p(x)=0) का मूल है / (2) is a root of (p(x)=0)
Step 1
Concept
(p(2)=0) means the equation is satisfied when (x=2). Substitution is the key method in such questions.
Step 2
Why this answer is correct
The correct answer is A. (2) (p(x)=0) का मूल है / (2) is a root of (p(x)=0). (p(2)=0) means the equation is satisfied when (x=2). Substitution is the key method in such questions.
Step 3
Exam Tip
(p(2)=0) का अर्थ है कि (x=2) रखने पर समीकरण संतुष्ट होता है। ऐसे प्रश्न में प्रतिस्थापन मुख्य तरीका है।
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यदि \(x^2-15x+56=0\), तो (x=7) रखने पर बायां पक्ष क्या बनेगा?
If \(x^2-15x+56=0\), what will the left side become when (x=7)?
#quadratic-equations
#substitution
#root-verification
#medium
A (0)
B (7)
C (-7)
D (14)
Explanation opens after your attempt
Step 1
Concept
\(7^2-15\cdot7+56=49-105+56=0\). 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). \(7^2-15\cdot7+56=49-105+56=0\). If the left side becomes (0), the given value is a root.
Step 3
Exam Tip
\(7^2-15\cdot7+56=49-105+56=0\) है। बायां पक्ष (0) हो तो दिया मान मूल है।
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क्या (x=5) समीकरण \(x^2-6x+5=0\) का मूल है?
Is (x=5) a root of \(x^2-6x+5=0\)?
#quadratic-equations
#root-check
#substitution
#medium
A हाँ / Yes
B नहीं / No
C केवल (x=1) मूल है / Only (x=1) 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=5) gives (25-30+5=0). Substitution is the simple way to check a root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=5) gives (25-30+5=0). Substitution is the simple way to check a root.
Step 3
Exam Tip
(x=5) रखने पर (25-30+5=0) मिलता है। मूल जांचने का सरल तरीका प्रतिस्थापन है।
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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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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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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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क्या (x=3) समीकरण \(x^2-4x+3=0\) का मूल है?
Is (x=3) a root of \(x^2-4x+3=0\)?
#quadratic-equations
#root-check
#substitution
#medium
A हाँ / Yes
B नहीं / No
C केवल (x=1) मूल है / Only (x=1) is a root
D निर्धारित नहीं हो सकता / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=3) gives (9-12+3=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=3) gives (9-12+3=0). To check a root, substitute the given value directly.
Step 3
Exam Tip
(x=3) रखने पर (9-12+3=0) मिलता है। मूल जांचने के लिए दिए मान को सीधे समीकरण में रखें।
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यदि (x=2) है तो \(x^2+5x-14=0\) में बायां पक्ष कितना होगा?
If (x=2), what is the left side of \(x^2+5x-14=0\)?
#quadratic equations
#substitution
#root
A (0)
B (2)
C (4)
D (-14)
Explanation opens after your attempt
Step 1
Concept
Substituting gives \(2^2+5\cdot2-14=0\). So (2) is a solution.
Step 2
Why this answer is correct
The correct answer is A. (0). Substituting gives \(2^2+5\cdot2-14=0\). So (2) is a solution.
Step 3
Exam Tip
रखने पर \(2^2+5\cdot2-14=0\) मिलता है। इसलिए (2) एक हल है।
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कौन सा मान \(x^2-3x-10=0\) का हल है?
Which value is a solution of \(x^2-3x-10=0\)?
#quadratic equations
#solution check
#substitution
A (1)
B (2)
C (5)
D (10)
Explanation opens after your attempt
Step 1
Concept
Since \(5^2-3\cdot5-10=0\), (x=5) is a solution.
Step 2
Why this answer is correct
The correct answer is C. (5). Since \(5^2-3\cdot5-10=0\), (x=5) is a solution.
Step 3
Exam Tip
\(5^2-3\cdot5-10=0\) है। इसलिए (x=5) हल है।
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कौन सा मान \(x^2-25=0\) का एक हल है?
Which value is one solution of \(x^2-25=0\)?
#quadratic equations
#solution
#substitution
A (2)
B (5)
C (7)
D (10)
Explanation opens after your attempt
Step 1
Concept
Since \(5^2-25=0\), (5) is a solution of this equation.
Step 2
Why this answer is correct
The correct answer is B. (5). Since \(5^2-25=0\), (5) is a solution of this equation.
Step 3
Exam Tip
\(5^2-25=0\) है। इसलिए (5) इस समीकरण का हल है।
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यदि (x=3) है तो \(x^2-4x+3=0\) में बायां पक्ष कितना होगा?
If (x=3), what is the left side of \(x^2-4x+3=0\)?
#quadratic equations
#substitution
#solution check
A (0)
B (3)
C (6)
D (-3)
Explanation opens after your attempt
Step 1
Concept
Substitution gives \(3^2-4\cdot3+3=0\). So (x=3) is a solution.
Step 2
Why this answer is correct
The correct answer is A. (0). Substitution gives \(3^2-4\cdot3+3=0\). So (x=3) is a solution.
Step 3
Exam Tip
रखने पर \(3^2-4\cdot3+3=0\) मिलता है। इसलिए (x=3) हल है।
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कौन सा समीकरण (x=0) को हल के रूप में रखता है?
Which equation has (x=0) as a solution?
#quadratic equations
#zero solution
#substitution
A \(x^2+5x=0\)
B \(x^2+5=0\)
C \(x^2-5=0\)
D \(x^2+5x+1=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+5x=0\)
Step 1
Concept
Putting (x=0) in option (A) gives (0=0). Direct substitution is the simplest way to check a solution.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+5x=0\). Putting (x=0) in option (A) gives (0=0). Direct substitution is the simplest way to check a solution.
Step 3
Exam Tip
(x=0) रखने पर विकल्प (A) में (0=0) मिलता है। हल जांचने का सबसे सरल तरीका प्रत्यक्ष प्रतिस्थापन है।
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यदि (x=1) है तो \(x^2+2x-3=0\) में बायां पक्ष कितना होगा?
If (x=1), what is the left side of \(x^2+2x-3=0\)?
#quadratic equations
#substitution
#solution
A (0)
B (1)
C (2)
D \(-3\)
Explanation opens after your attempt
Step 1
Concept
Substituting gives \(1^2+2\cdot1-3=0\). So (1) is a solution.
Step 2
Why this answer is correct
The correct answer is A. (0). Substituting gives \(1^2+2\cdot1-3=0\). So (1) is a solution.
Step 3
Exam Tip
रखने पर \(1^2+2\cdot1-3=0\) मिलता है। इसलिए (1) एक हल है।
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कौन सा मान \(x^2+x-6=0\) का हल है?
Which value is a solution of \(x^2+x-6=0\)?
#quadratic equations
#root checking
#substitution
A (1)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
Since \(2^2+2-6=0\), (x=2) is a solution of the equation.
Step 2
Why this answer is correct
The correct answer is B. (2). Since \(2^2+2-6=0\), (x=2) is a solution of the equation.
Step 3
Exam Tip
\(2^2+2-6=0\) है। इसलिए (x=2) इस समीकरण का हल है।
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समीकरण \(x^2-4x+4=0\) में (x=2) रखने पर क्या मिलता है?
What do we get by putting (x=2) in \(x^2-4x+4=0\)?
#quadratic equations
#substitution
#perfect square
A (0=0)
B (2=0)
C (4=0)
D \(-4=0\)
Explanation opens after your attempt
Step 1
Concept
We get \(2^2-4\cdot2+4=0\). Hence (x=2) is a correct solution.
Step 2
Why this answer is correct
The correct answer is A. (0=0). We get \(2^2-4\cdot2+4=0\). Hence (x=2) is a correct solution.
Step 3
Exam Tip
\(2^2-4\cdot2+4=0\) है। अतः (x=2) सही हल है।
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यदि (x=2) है तो \(x^2-5x+6=0\) में बायां पक्ष कितना होगा?
If (x=2), what is the left side of \(x^2-5x+6=0\)?
#quadratic equations
#substitution
#root checking
A (0)
B (2)
C \(-2\)
D (6)
Explanation opens after your attempt
Step 1
Concept
Substitution gives \(2^2-5\cdot2+6=0\). So (x=2) is a solution.
Step 2
Why this answer is correct
The correct answer is A. (0). Substitution gives \(2^2-5\cdot2+6=0\). So (x=2) is a solution.
Step 3
Exam Tip
रखने पर \(2^2-5\cdot2+6=0\) मिलता है। इसलिए (x=2) समीकरण का हल है।
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यदि \(x=\sqrt{3}\), तो \(2x^2-x-6\) का मान क्या है?
If \(x=\sqrt{3}\), what is the value of \(2x^2-x-6\)?
#polynomial value
#substitution
#irrational
A \(-\sqrt{3}\)
B (0)
C \(\sqrt{3}\)
D \(6-\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(-\sqrt{3}\)
Step 1
Concept
\(2x^2-x-6=2\cdot3-\sqrt{3}-6=-\sqrt{3}\). Simplify \(x^2\) first in exams.
Step 2
Why this answer is correct
The correct answer is A. \(-\sqrt{3}\). \(2x^2-x-6=2\cdot3-\sqrt{3}-6=-\sqrt{3}\). Simplify \(x^2\) first in exams.
Step 3
Exam Tip
\(2x^2-x-6=2\cdot3-\sqrt{3}-6=-\sqrt{3}\) है। परीक्षा में \(x^2\) को पहले सरल करें।
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यदि \(x=3-\sqrt{2}\), तो \(x^2-6x+7\) का मान क्या है?
If \(x=3-\sqrt{2}\), what is the value of \(x^2-6x+7\)?
#polynomial identity
#irrational root
#substitution
A (0)
B \(2\sqrt{2}\)
C (7)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Since \(x-3=-\sqrt{2}\), ((x-3)2 =2), hence \(x^2-6x+7=0\). Handle \(a-\sqrt{b}\) the same way in exams.
Step 2
Why this answer is correct
The correct answer is A. (0). Since \(x-3=-\sqrt{2}\), ((x-3)2 =2), hence \(x^2-6x+7=0\). Handle \(a-\sqrt{b}\) the same way in exams.
Step 3
Exam Tip
\(x-3=-\sqrt{2}\), इसलिए ((x-3)2 =2) से \(x^2-6x+7=0\) है। परीक्षा में \(a-\sqrt{b}\) को भी इसी विधि से संभालें।
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