If the zeros of the polynomial \(p(x)=x^2+ax+b\) are \(-4\) and \(1\), what is the value of \(b\)?
Answer and explanation
Correct answer: -4
Since the polynomial is monic and its zeros are \(-4\) and \(1\), we can write \(p(x)=(x+4)(x-1)\). Expanding gives \(p(x)=x^2+3x-4\), so the constant term is \(b=-4\). The value \(4\) is incorrect because the constant term equals the product of the zeros, not their sum. Exam tip: For \(x^2+ax+b\), the product of the zeros is directly equal to \(b\).
Frequently asked questions
What is the correct answer to this question?
-4
Why is this the correct answer?
Since the polynomial is monic and its zeros are \(-4\) and \(1\), we can write \(p(x)=(x+4)(x-1)\). Expanding gives \(p(x)=x^2+3x-4\), so the constant term is \(b=-4\). The value \(4\) is incorrect because the constant term equals the product of the zeros, not their sum. Exam tip: For \(x^2+ax+b\), the product of the zeros is directly equal to \(b\).
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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