If \(p(x)=x^2+ax+b\) is a quadratic polynomial such that \(p(-1)=0\) and \(p(5)=0\), what is the value of \(b\)?
Answer and explanation
Correct answer: \(-5\)
Since \(-1\) and \(5\) are the zeroes of \(p(x)\), we can write \(p(x)=(x+1)(x-5)=x^2-4x-5\). Comparing this with \(x^2+ax+b\), the constant term is \(b=-5\). Therefore, option A is correct. Exam tip: For a monic quadratic polynomial, the product of its zeroes equals its constant term.
Frequently asked questions
What is the correct answer to this question?
\(-5\)
Why is this the correct answer?
Since \(-1\) and \(5\) are the zeroes of \(p(x)\), we can write \(p(x)=(x+1)(x-5)=x^2-4x-5\). Comparing this with \(x^2+ax+b\), the constant term is \(b=-5\). Therefore, option A is correct. Exam tip: For a monic quadratic polynomial, the product of its zeroes equals its constant term.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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