Question 1/7
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि \(x^2-7x+10=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\frac{\alpha+2}{\alpha-2}+\frac{\beta+2}{\beta-2}\) का मान क्या है?
If \(\alpha,\beta\) are the roots of \(x^2-7x+10=0\), what is \(\frac{\alpha+2}{\alpha-2}+\frac{\beta+2}{\beta-2}\)?
#quadratic-roots
#undefined-expression
#root-check
A अपरिभाषित / Undefined
B (7)
C (9)
D \(\frac{22}{3}\)
Explanation opens after your attempt
Correct Answer
A. अपरिभाषित / Undefined
Step 1
Concept
One root can be \(\alpha=2\), which makes \(\alpha-2=0\). Therefore the expression is undefined; always check zero denominators first in exams.
Step 2
Why this answer is correct
The correct answer is A. अपरिभाषित / Undefined. One root can be \(\alpha=2\), which makes \(\alpha-2=0\). Therefore the expression is undefined; always check zero denominators first in exams.
Step 3
Exam Tip
जड़ों में से एक \(\alpha=2\) हो सकती है, जिससे \(\alpha-2=0\) बनता है। इसलिए व्यंजक अपरिभाषित है; परीक्षा में हर पहले शून्य हर देखें।
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Question 2/7
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
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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Question 3/7
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 4/7
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 5/7
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 6/7
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
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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Question 7/7
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
क्या (x=1) समीकरण \(x^2-x=0\) का मूल है?
Is (x=1) a root of \(x^2-x=0\)?
#quadratic-equations
#root-check
#easy
A हाँ / Yes
B नहीं / No
C केवल (x=0) मूल है / Only (x=0) is a root
D कोई मूल नहीं है / There is no root
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=1) gives \(1^2-1=0\). To check a root, directly substitute the given value.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=1) gives \(1^2-1=0\). To check a root, directly substitute the given value.
Step 3
Exam Tip
(x=1) रखने पर \(1^2-1=0\) मिलता है। मूल की जांच में दिया हुआ मान सीधे रखें।
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