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If \(p(x)=x^2+ax+a\) and \(p(1)=5\), what is the value of \(a\)?
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Answer and explanation
Correct answer: 2
Substitute \(x=1\) into the polynomial: \(p(1)=1^2+a(1)+a=1+2a\). Since \(p(1)=5\), we get \(1+2a=5\), so \(2a=4\) and \(a=2\). Hence, option B is correct. Exam tip: When \(p(k)\) is given, substitute \(x=k\) directly to form an equation.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
Substitute \(x=1\) into the polynomial: \(p(1)=1^2+a(1)+a=1+2a\). Since \(p(1)=5\), we get \(1+2a=5\), so \(2a=4\) and \(a=2\). Hence, option B is correct. Exam tip: When \(p(k)\) is given, substitute \(x=k\) directly to form an equation.
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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