If the roots of (x^2+px+q=0) are (p) and (q) themselves, which relation is correct?
Answer and explanation
Correct answer: (p+q=-p) and (pq=q)
For a monic quadratic \(x^2+px+q=0\), the sum of the roots is \(-p\), and their product is \(q\). The question says that the roots themselves are \(p\) and \(q\). Substituting these names into the root relations gives \(p+q=-p\) for the sum and \(pq=q\) for the product. These are exactly the two statements in option A.
The symbols \(p\) and \(q\) play two roles here: they are coefficients and, according to the condition, also root values. That is unusual but valid. The relations do not require solving for particular numerical values; they follow directly from Vieta’s formulas. Options B, C, and D alter one or both signs or products, so they do not match the standard coefficient-root relations. Hence A is correct.
Frequently asked questions
What is the correct answer to this question?
(p+q=-p) and (pq=q)
Why is this the correct answer?
For a monic quadratic \(x^2+px+q=0\), the sum of the roots is \(-p\), and their product is \(q\). The question says that the roots themselves are \(p\) and \(q\). Substituting these names into the root relations gives \(p+q=-p\) for the sum and \(pq=q\) for the product. These are exactly the two statements in option A.
The symbols \(p\) and \(q\) play two roles here: they are coefficients and, according to the condition, also root values. That is unusual but valid. The relations do not require solving for particular numerical values; they follow directly from Vieta’s formulas. Options B, C, and D alter one or both signs or products, so they do not match the standard coefficient-root relations. Hence A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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