Question 1/6
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
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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Question 2/6
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
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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Question 3/6
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
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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Question 4/6
Medium Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
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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Question 5/6
Easy Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
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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Question 6/6
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
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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