Which of the following expresses the equation \(x^2+6x+9=0\) in factorised form?
Answer and explanation
Correct answer: \((x+3)^2=0\)
\(x^2+6x+9\) is a perfect-square trinomial. Comparing with \((x+a)^2=x^2+2ax+a^2\) gives \(2a=6\), so \(a=3\) and the trinomial equals \((x+3)^2\). Hence the equation factors as \((x+3)^2=0\). Option B is incorrect because \((x-3)^2\) would produce a middle term of \(-6x\); options C and D have wrong constant terms. Exam tip: identify perfect squares by checking if the constant equals the square of half the middle coefficient (i.e., check if constant = (middle/2)^2).
Frequently asked questions
What is the correct answer to this question?
\((x+3)^2=0\)
Why is this the correct answer?
\(x^2+6x+9\) is a perfect-square trinomial. Comparing with \((x+a)^2=x^2+2ax+a^2\) gives \(2a=6\), so \(a=3\) and the trinomial equals \((x+3)^2\). Hence the equation factors as \((x+3)^2=0\). Option B is incorrect because \((x-3)^2\) would produce a middle term of \(-6x\); options C and D have wrong constant terms. Exam tip: identify perfect squares by checking if the constant equals the square of half the middle coefficient (i.e., check if constant = (middle/2)^2).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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