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Class 10MathematicsPolynomialsPolynomials in one variableHardLevel 47
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If \(p(x)=2x^2+bx+c\), \(p(0)=5\), and \(p(1)=1\), what is the value of \(b\)?

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Answer and explanation

Correct answer: -6

Since \(p(0)=c=5\), substituting \(x=1\) gives \(p(1)=2+b+5=1\). Hence, \(b+7=1\) and \(b=-6\). The distractor \(-5\) results from an arithmetic error while solving this equation. Exam tip: for a polynomial, the constant term is obtained directly by evaluating it at \(x=0\).

Related tags

Polynomial EvaluationConstant TermQuadratic PolynomialLinear Equations

Frequently asked questions

What is the correct answer to this question?

-6

Why is this the correct answer?

Since \(p(0)=c=5\), substituting \(x=1\) gives \(p(1)=2+b+5=1\). Hence, \(b+7=1\) and \(b=-6\). The distractor \(-5\) results from an arithmetic error while solving this equation. Exam tip: for a polynomial, the constant term is obtained directly by evaluating it at \(x=0\).

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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