किस विकल्प में (x=1) और (x=4) मूल हैं?
Which option has roots (x=1) and (x=4)?
Explanation opens after your attempt
Correct Answer
A. \(x^2-5x+4=0\)
Step 1
Concept
If the roots are (1) and (4), the factors are ((x-1)) and ((x-4)). Their product gives \(x^2-5x+4=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-5x+4=0\). If the roots are (1) and (4), the factors are ((x-1)) and ((x-4)). Their product gives \(x^2-5x+4=0\).
Step 3
Exam Tip
मूल (1) और (4) हों तो गुणनखंड ((x-1)) और ((x-4)) होंगे। इनका गुणन \(x^2-5x+4=0\) देता है।
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यदि किसी द्विघात समीकरण में (a=2), (b=-7), (c=3) हैं, तो समीकरण कौन-सा है?
If a quadratic equation has (a=2), (b=-7), (c=3), which equation is it?
Explanation opens after your attempt
Correct Answer
B. \(2x^2-7x+3=0\)
Step 1
Concept
Substituting in \(ax^2+bx+c=0\) gives \(2x^2-7x+3=0\). Keep the negative sign of (b).
Step 2
Why this answer is correct
The correct answer is B. \(2x^2-7x+3=0\). Substituting in \(ax^2+bx+c=0\) gives \(2x^2-7x+3=0\). Keep the negative sign of (b).
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(2x^2-7x+3=0\) मिलता है। (b) का ऋण चिन्ह साथ रखें।
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यदि (a=3,\ b=0,\ c=-12) हैं तो संबंधित द्विघात समीकरण कौन-सा है?
If (a=3,\ b=0,\ c=-12), which is the corresponding quadratic equation?
Explanation opens after your attempt
Correct Answer
A. \(3x^2-12=0\)
Step 1
Concept
Substituting in \(ax^2+bx+c=0\) gives \(3x^2+0x-12=0\). Simplifying gives \(3x^2-12=0\).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-12=0\). Substituting in \(ax^2+bx+c=0\) gives \(3x^2+0x-12=0\). Simplifying gives \(3x^2-12=0\).
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(3x^2+0x-12=0\) मिलता है। इसे सरल करने पर \(3x^2-12=0\) है।
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जिन मूलों में (0) और (-3) हों उनके लिए सही द्विघात समीकरण कौन-सा है?
Which quadratic equation has roots (0) and (-3)?
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x=0\)
Step 1
Concept
For roots (0) and (-3), the factors are (x) and (x+3). So the equation is (x(x+3)=0), that is \(x^2+3x=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x=0\). For roots (0) and (-3), the factors are (x) and (x+3). So the equation is (x(x+3)=0), that is \(x^2+3x=0\).
Step 3
Exam Tip
मूल (0) और (-3) होने पर गुणनखंड (x) और (x+3) होंगे। इसलिए समीकरण (x(x+3)=0) यानी \(x^2+3x=0\) है।
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किसी संख्या का वर्ग उस संख्या के (5) गुने से (6) अधिक है। यदि संख्या (x) है तो समीकरण क्या होगा?
The square of a number is (6) more than (5) times the number. If the number is (x), what is the equation?
Explanation opens after your attempt
Correct Answer
A. \(x^2=5x+6\)
Step 1
Concept
The square is \(x^2\), and (6) more than (5) times the number is (5x+6). So the equation is \(x^2=5x+6\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2=5x+6\). The square is \(x^2\), and (6) more than (5) times the number is (5x+6). So the equation is \(x^2=5x+6\).
Step 3
Exam Tip
संख्या का वर्ग \(x^2\) और (5) गुने से (6) अधिक (5x+6) है। इसलिए समीकरण \(x^2=5x+6\) बनेगा।
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यदि (a=2), (b=0), (c=-18) हैं तो समीकरण क्या होगा?
If (a=2), (b=0), (c=-18), what is the equation?
Explanation opens after your attempt
Correct Answer
A. \(2x^2-18=0\)
Step 1
Concept
Substituting in standard form gives \(2x^2+0x-18=0\). This is written as \(2x^2-18=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-18=0\). Substituting in standard form gives \(2x^2+0x-18=0\). This is written as \(2x^2-18=0\).
Step 3
Exam Tip
मानक रूप में रखने पर \(2x^2+0x-18=0\) मिलता है। इसे \(2x^2-18=0\) लिखते हैं।
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कौन सा रूप (a=3), (b=-4), (c=-2) को दर्शाता है?
Which form represents (a=3), (b=-4), (c=-2)?
Explanation opens after your attempt
Correct Answer
A. \(3x^2-4x-2=0\)
Step 1
Concept
Putting the values in \(ax^2+bx+c=0\) gives \(3x^2-4x-2=0\). Watch the sign of (b).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-4x-2=0\). Putting the values in \(ax^2+bx+c=0\) gives \(3x^2-4x-2=0\). Watch the sign of (b).
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(3x^2-4x-2=0\) मिलता है। (b) का चिन्ह ध्यान रखें।
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यदि (a=1), (b=0), (c=-25) हैं तो समीकरण क्या होगा?
If (a=1), (b=0), (c=-25), what is the equation?
Explanation opens after your attempt
Correct Answer
A. \(x^2-25=0\)
Step 1
Concept
Substituting in \(ax^2+bx+c=0\) gives \(x^2+0x-25=0\). This is written as \(x^2-25=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-25=0\). Substituting in \(ax^2+bx+c=0\) gives \(x^2+0x-25=0\). This is written as \(x^2-25=0\).
Step 3
Exam Tip
\(ax^2+bx+c=0\) में रखने पर \(x^2+0x-25=0\) मिलता है। इसे \(x^2-25=0\) लिखते हैं।
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कौन सा रूप \(ax^2+bx+c=0\) में (a=2), (b=-5), (c=3) को दर्शाता है?
Which form represents (a=2), (b=-5), (c=3) in \(ax^2+bx+c=0\)?
Explanation opens after your attempt
Correct Answer
A. \(2x^2-5x+3=0\)
Step 1
Concept
Putting the given values in standard form gives \(2x^2-5x+3=0\). Keep the sign of (b) carefully.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-5x+3=0\). Putting the given values in standard form gives \(2x^2-5x+3=0\). Keep the sign of (b) carefully.
Step 3
Exam Tip
दिए गए मान सीधे मानक रूप में रखने पर \(2x^2-5x+3=0\) मिलता है। (b) का चिन्ह ध्यान रखें।
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