If the roots of (x^2+px+q=0) are (2) and (p), which relation involving (q) is correct?
Answer and explanation
Correct answer: (q=2p)
For the monic quadratic equation (x^2+px+q=0), the product of the roots equals the constant term (q). Since the roots are (2) and (p), (q=2\times p=2p). Also, their sum gives (2+p=-p), so (p=-1) and (q=-2), confirming the relation. Exam tip: In (x^2+ax+b=0), the sum of roots is (-a) and their product is (b).
Frequently asked questions
What is the correct answer to this question?
(q=2p)
Why is this the correct answer?
For the monic quadratic equation (x^2+px+q=0), the product of the roots equals the constant term (q). Since the roots are (2) and (p), (q=2\times p=2p). Also, their sum gives (2+p=-p), so (p=-1) and (q=-2), confirming the relation. Exam tip: In (x^2+ax+b=0), the sum of roots is (-a) and their product is (b).
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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