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If \(p(x)=3x^2+bx+c\), \(p(0)=7\), and \(p(1)=2\), what is the value of \(b\)?
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Answer and explanation
Correct answer: -8
Since \(p(0)=c\), we get \(c=7\). Substituting \(x=1\) gives \(p(1)=3+b+c=2\), so \(3+b+7=2\) and hence \(b=-8\). Option B, \(-7\), results from omitting the contribution of the term \(3x^2\). Exam tip: substituting \(x=0\) in a polynomial directly gives its constant term.
Frequently asked questions
What is the correct answer to this question?
-8
Why is this the correct answer?
Since \(p(0)=c\), we get \(c=7\). Substituting \(x=1\) gives \(p(1)=3+b+c=2\), so \(3+b+7=2\) and hence \(b=-8\). Option B, \(-7\), results from omitting the contribution of the term \(3x^2\). Exam tip: substituting \(x=0\) in a polynomial directly gives 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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