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If the polynomial \(p(x)=x^3+rx^2+s\) satisfies \(p(0)=5\) and \(p(1)=9\), what is the value of \(r\)?
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Answer and explanation
Correct answer: 3
Substituting \(x=0\) gives \(p(0)=s=5\). Then, substituting \(x=1\), \(p(1)=1+r+5=9\), so \(r=3\). Therefore, option C is correct. Exam tip: when evaluating a polynomial at zero, all terms containing \(x\) vanish, leaving only the constant term.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Substituting \(x=0\) gives \(p(0)=s=5\). Then, substituting \(x=1\), \(p(1)=1+r+5=9\), so \(r=3\). Therefore, option C is correct. Exam tip: when evaluating a polynomial at zero, all terms containing \(x\) vanish, leaving only the 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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