If the roots of \\(x^2+px+q=0\\) are 1 and \\(p\\), which relation for \\(q\\) is correct?
Answer and explanation
Correct answer: \\(q=p\\)
For the quadratic equation \\(x^2+px+q=0\\), the product of the roots equals the constant term \\(q\\). Since the roots are 1 and \\(p\\), \\(q=1\cdot p=p\\). The sum condition also gives \\(1+p=-p\\), so \\(p=-\\frac{1}{2}\\); nevertheless, the required relation remains \\(q=p\\). Exam tip: In \\(x^2+bx+c=0\\), the product of the roots is always \\(c\\).
Frequently asked questions
What is the correct answer to this question?
\\(q=p\\)
Why is this the correct answer?
For the quadratic equation \\(x^2+px+q=0\\), the product of the roots equals the constant term \\(q\\). Since the roots are 1 and \\(p\\), \\(q=1\cdot p=p\\). The sum condition also gives \\(1+p=-p\\), so \\(p=-\\frac{1}{2}\\); nevertheless, the required relation remains \\(q=p\\). Exam tip: In \\(x^2+bx+c=0\\), the product of the roots is always \\(c\\).
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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