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If \(x^2+10x+k\) is a perfect square and can be written as \((x+5)^2\), what is the value of \(k\)?
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Answer and explanation
Correct answer: 25
\((x+5)^2=x^2+2(5)x+5^2=x^2+10x+25\). Comparing this with \(x^2+10x+k\) gives \(k=25\). The distractor 5 is the constant inside the bracket, whereas \(k\) is its square. Exam tip: in \((x+a)^2=x^2+2ax+a^2\), the constant term is \(a^2\).
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What is the correct answer to this question?
25
Why is this the correct answer?
\((x+5)^2=x^2+2(5)x+5^2=x^2+10x+25\). Comparing this with \(x^2+10x+k\) gives \(k=25\). The distractor 5 is the constant inside the bracket, whereas \(k\) is its square. Exam tip: in \((x+a)^2=x^2+2ax+a^2\), the constant term is \(a^2\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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