यदि \(x^2+bx+c=0\) की जड़ें एक-दूसरे की विपरीत संख्याएँ हैं, तो कौन-सी शर्त अनिवार्य है?
If the roots of \(x^2+bx+c=0\) are opposites of each other, which condition is necessary?
Explanation opens after your attempt
Step 1
Concept
Opposite roots have sum (0). Here the sum is (-b), so (b=0).
Step 2
Why this answer is correct
The correct answer is A. (b=0). Opposite roots have sum (0). Here the sum is (-b), so (b=0).
Step 3
Exam Tip
विपरीत जड़ों का योग (0) होता है। यहाँ योग (-b) है, इसलिए (b=0)।
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यदि किसी द्विघात समीकरण के मूल (c) और (-c) हैं तो अचर पद और अग्र गुणांक के अनुपात \(\frac{d}{a}\) का मान क्या होगा?
If the roots of a quadratic equation are (c) and (-c), what is the value of the ratio \(\frac{d}{a}\) of constant term to leading coefficient?
Explanation opens after your attempt
Correct Answer
A. \(-c^2\)
Step 1
Concept
\(\frac{d}{a}\) is the product of roots. Here (c(-c)=-c-2).
Step 2
Why this answer is correct
The correct answer is A. \(-c^2\). \(\frac{d}{a}\) is the product of roots. Here (c(-c)=-c-2).
Step 3
Exam Tip
\(\frac{d}{a}\) मूलों का गुणनफल होता है। यहां (c(-c)=-c-2) है।
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यदि किसी द्विघात समीकरण के मूल (b) और (-b) हैं तो अचर पद और अग्र गुणांक के अनुपात \(\frac{c}{a}\) का मान क्या होगा?
If the roots of a quadratic equation are (b) and (-b), what is the value of the ratio \(\frac{c}{a}\) of constant term to leading coefficient?
Explanation opens after your attempt
Correct Answer
A. \(-b^2\)
Step 1
Concept
\(\frac{c}{a}\) is the product of roots. Here (b(-b)=-b-2).
Step 2
Why this answer is correct
The correct answer is A. \(-b^2\). \(\frac{c}{a}\) is the product of roots. Here (b(-b)=-b-2).
Step 3
Exam Tip
\(\frac{c}{a}\) मूलों का गुणनफल होता है। यहां (b(-b)=-b-2) है।
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यदि किसी द्विघात समीकरण के मूल (a) और (-a) हैं तो अचर पद और अग्र गुणांक के अनुपात \(\frac{c}{a_1}\) का मान क्या होगा?
If the roots of a quadratic equation are (a) and (-a), what is the value of the ratio \(\frac{c}{a_1}\) of constant term to leading coefficient?
Explanation opens after your attempt
Correct Answer
A. \(-a^2\)
Step 1
Concept
\(\frac{c}{a_1}\) is the product of roots. Here (a(-a)=-a-2).
Step 2
Why this answer is correct
The correct answer is A. \(-a^2\). \(\frac{c}{a_1}\) is the product of roots. Here (a(-a)=-a-2).
Step 3
Exam Tip
\(\frac{c}{a_1}\) मूलों का गुणनफल होता है। यहां (a(-a)=-a-2) है।
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यदि किसी द्विघात समीकरण के मूल (r) और (-r) हैं तो उनके योग का मान क्या होगा?
If the roots of a quadratic equation are (r) and (-r), what is their sum?
Explanation opens after your attempt
Step 1
Concept
(r+(-r)=0). The sum of opposite roots is always (0).
Step 2
Why this answer is correct
The correct answer is C. (0). (r+(-r)=0). The sum of opposite roots is always (0).
Step 3
Exam Tip
(r+(-r)=0) होता है। विपरीत मूलों का योग हमेशा (0) होता है।
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किस समीकरण के दोनों मूल विपरीत संख्याएँ होंगे?
Which equation will have roots that are opposite numbers?
Explanation opens after your attempt
Correct Answer
A. \(x^2-16=0\)
Step 1
Concept
\(x^2-16=0\) gives \(x=\pm4\), which are opposite numbers. Pure quadratics often give opposite roots.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-16=0\). \(x^2-16=0\) gives \(x=\pm4\), which are opposite numbers. Pure quadratics often give opposite roots.
Step 3
Exam Tip
\(x^2-16=0\) से \(x=\pm4\) मिलता है, जो विपरीत संख्याएँ हैं। शुद्ध द्विघात में अक्सर विपरीत मूल मिलते हैं।
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