In which of the following perfect-square forms can the equation \(4x^2-12x+9=0\) be written?
Answer and explanation
Correct answer: \((2x-3)^2=0\)
Using the identity \((a-b)^2=a^2-2ab+b^2\), we get \(4x^2-12x+9=(2x-3)^2\). Hence the equation becomes \((2x-3)^2=0\). In option B, the middle term would be positive, whereas the given middle term is \(-12x\). In exams, take the square roots of the first and last terms and then verify the middle term.
Frequently asked questions
What is the correct answer to this question?
\((2x-3)^2=0\)
Why is this the correct answer?
Using the identity \((a-b)^2=a^2-2ab+b^2\), we get \(4x^2-12x+9=(2x-3)^2\). Hence the equation becomes \((2x-3)^2=0\). In option B, the middle term would be positive, whereas the given middle term is \(-12x\). In exams, take the square roots of the first and last terms and then verify the middle term.
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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