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For which value of \(x\) does the polynomial \(p(x)=x^2+4x+5\) attain its minimum value?
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Answer and explanation
Correct answer: \(x=-2\)
Completing the square gives \(p(x)=x^2+4x+5=(x+2)^2+1\). Since \((x+2)^2\geq 0\), the expression is smallest when \(x+2=0\), so \(x=-2\). Hence, option B is correct. Exam tip: write a quadratic in the form \(a(x-h)^2+k\); when \(a>0\), its minimum occurs at \(x=h\).
Frequently asked questions
What is the correct answer to this question?
\(x=-2\)
Why is this the correct answer?
Completing the square gives \(p(x)=x^2+4x+5=(x+2)^2+1\). Since \((x+2)^2\geq 0\), the expression is smallest when \(x+2=0\), so \(x=-2\). Hence, option B is correct. Exam tip: write a quadratic in the form \(a(x-h)^2+k\); when \(a>0\), its minimum occurs at \(x=h\).
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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