Question 1/10
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
(x-2 -(a+8)x+8a=0) के बारे में कौन-सा कथन हमेशा सही है?
Which statement is always correct about (x-2 -(a+8)x+8a=0)?
#quadratic-roots
#parametric-equation
#root-verification
A (8) हमेशा एक जड़ है / (8) is always one root
B (a+8) हमेशा एक जड़ है / (a+8) is always one root
C दोनों जड़ें हमेशा (8) हैं / Both roots are always (8)
D जड़ें कभी वास्तविक नहीं हैं / The roots are never real
Explanation opens after your attempt
Correct Answer
A. (8) हमेशा एक जड़ है / (8) is always one root
Step 1
Concept
Putting (x=8) gives (64-8(a+8)+8a=0). Hence (8) is always one root and the other root is (a).
Step 2
Why this answer is correct
The correct answer is A. (8) हमेशा एक जड़ है / (8) is always one root. Putting (x=8) gives (64-8(a+8)+8a=0). Hence (8) is always one root and the other root is (a).
Step 3
Exam Tip
(x=8) रखने पर (64-8(a+8)+8a=0) मिलता है। इसलिए (8) हमेशा एक जड़ है और दूसरी जड़ (a) है।
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Question 2/10
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
(x-2 -(a+6)x+6a=0) के लिए कौन-सा कथन हमेशा सत्य है?
Which statement is always true for (x-2 -(a+6)x+6a=0)?
#quadratic-roots
#root-verification
#parametric-equation
A (a+6) हमेशा जड़ है / (a+6) is always a root
B (6) हमेशा जड़ है / (6) is always a root
C दोनों जड़ें हमेशा समान हैं / Both roots are always equal
D जड़ें कभी वास्तविक नहीं हैं / The roots are never real
Explanation opens after your attempt
Correct Answer
B. (6) हमेशा जड़ है / (6) is always a root
Step 1
Concept
Putting (x=6) gives (36-6(a+6)+6a=0). Hence (6) is always one root and the other root is (a).
Step 2
Why this answer is correct
The correct answer is B. (6) हमेशा जड़ है / (6) is always a root. Putting (x=6) gives (36-6(a+6)+6a=0). Hence (6) is always one root and the other root is (a).
Step 3
Exam Tip
(x=6) रखने पर (36-6(a+6)+6a=0) मिलता है। इसलिए (6) हमेशा एक जड़ है और दूसरी जड़ (a) है।
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Question 3/10
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
(x-2 -(a+4)x+4a=0) के लिए कौन-सा कथन हमेशा सत्य है?
Which statement is always true for (x-2 -(a+4)x+4a=0)?
#quadratic-roots
#root-verification
#identity
A (4) हमेशा एक जड़ है / (4) is always a root
B (a+4) हमेशा एक जड़ है / (a+4) is always a root
C दोनों जड़ें हमेशा समान हैं / Both roots are always equal
D जड़ें कभी वास्तविक नहीं हैं / The roots are never real
Explanation opens after your attempt
Correct Answer
A. (4) हमेशा एक जड़ है / (4) is always a root
Step 1
Concept
Putting (x=4) gives (16-4(a+4)+4a=0). Hence (4) is always one root and the other root is (a).
Step 2
Why this answer is correct
The correct answer is A. (4) हमेशा एक जड़ है / (4) is always a root. Putting (x=4) gives (16-4(a+4)+4a=0). Hence (4) is always one root and the other root is (a).
Step 3
Exam Tip
(x=4) रखने पर (16-4(a+4)+4a=0) मिलता है। अतः (4) हमेशा एक जड़ है और दूसरी जड़ (a) होती है।
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Question 4/10
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि (x=0), \(ax^2+bx+c=0\) की जड़ है, तो कौन-सी शर्त निश्चित रूप से सही है?
If (x=0) is a root of \(ax^2+bx+c=0\), which condition must be true?
#quadratic-roots
#zero-root
#root-verification
A (c=0)
B (b=0)
C (a=0)
D (a+b=0)
Explanation opens after your attempt
Step 1
Concept
Putting (x=0) gives (c=0). Thus the direct condition for zero to be a root is (c=0).
Step 2
Why this answer is correct
The correct answer is A. (c=0). Putting (x=0) gives (c=0). Thus the direct condition for zero to be a root is (c=0).
Step 3
Exam Tip
(x=0) रखने पर समीकरण (c=0) बनता है। इसलिए शून्य जड़ होने की सीधी शर्त (c=0) है।
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Question 5/10
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
(x-2 -(a+3)x+3a=0) के बारे में कौन-सा कथन हमेशा सही है?
Which statement is always true about (x-2 -(a+3)x+3a=0)?
#quadratic-roots
#root-verification
#parameter
A (3) हमेशा एक जड़ है / (3) is always a root
B (a) कभी जड़ नहीं है / (a) is never a root
C दोनों जड़ें हमेशा समान हैं / Both roots are always equal
D कोई वास्तविक जड़ नहीं है / There is no real root
Explanation opens after your attempt
Correct Answer
A. (3) हमेशा एक जड़ है / (3) is always a root
Step 1
Concept
Putting (x=3) gives (9-3(a+3)+3a=0). Hence (3) is always one root, and the other root is (a).
Step 2
Why this answer is correct
The correct answer is A. (3) हमेशा एक जड़ है / (3) is always a root. Putting (x=3) gives (9-3(a+3)+3a=0). Hence (3) is always one root, and the other root is (a).
Step 3
Exam Tip
(x=3) रखने पर (9-3(a+3)+3a=0) मिलता है। इसलिए (3) हमेशा एक जड़ है और दूसरी जड़ (a) होती है।
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Question 6/10
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि (x=2), \(kx^2-6x+4=0\) की जड़ है, तो (k) का मान क्या है?
If (x=2) is a root of \(kx^2-6x+4=0\), what is (k)?
#quadratic-roots
#root-verification
#parameter
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Putting (x=2), we get (4k-12+4=0). Hence (4k=8) and (k=2).
Step 2
Why this answer is correct
The correct answer is B. (2). Putting (x=2), we get (4k-12+4=0). Hence (4k=8) and (k=2).
Step 3
Exam Tip
(x=2) रखने पर (4k-12+4=0) मिलता है। इसलिए (4k=8) और (k=2)।
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Question 7/10
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
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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Question 8/10
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 9/10
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
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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Question 10/10
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
क्या (x=0) समीकरण \(x^2+5x=0\) का मूल है?
Is (x=0) a root of \(x^2+5x=0\)?
#quadratic-equations
#root-verification
#easy
A हाँ / Yes
B नहीं / No
C केवल (x=5) मूल है / Only (x=5) is a root
D केवल (x=-5) मूल है / Only (x=-5) is a root
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=0) gives \(0^2+5\cdot0=0\). Substitution is the easiest way to check a root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=0) gives \(0^2+5\cdot0=0\). Substitution is the easiest way to check a root.
Step 3
Exam Tip
(x=0) रखने पर \(0^2+5\cdot0=0\) मिलता है। मूल जांचने में प्रतिस्थापन सबसे आसान तरीका है।
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