If \(p(x)=x^2+kx+25\) is a perfect-square polynomial and \(k<0\), what is the value of \(k\)?
Answer and explanation
Correct answer: -10
A perfect-square form of \(x^2+kx+25\) must be \((x\pm5)^2\). Since \(k<0\), use \((x-5)^2=x^2-10x+25\), giving \(k=-10\). The form \((x+5)^2\) gives \(k=10\), but it does not satisfy the stated condition. Exam tip: in \((x+a)^2=x^2+2ax+a^2\), the coefficient of the middle term is \(2a\).
Frequently asked questions
What is the correct answer to this question?
-10
Why is this the correct answer?
A perfect-square form of \(x^2+kx+25\) must be \((x\pm5)^2\). Since \(k<0\), use \((x-5)^2=x^2-10x+25\), giving \(k=-10\). The form \((x+5)^2\) gives \(k=10\), but it does not satisfy the stated condition. Exam tip: in \((x+a)^2=x^2+2ax+a^2\), the coefficient of the middle term is \(2a\).
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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