In which of the following perfect-square forms can the equation \(49x^2-42x+9=0\) be written?
Answer and explanation
Correct answer: \((7x-3)^2=0\)
Using \((a-b)^2=a^2-2ab+b^2\), we get \((7x-3)^2=49x^2-42x+9\). Hence the equation becomes \((7x-3)^2=0\). In option B, the middle term would be \(+42x\), while options C and D have an incorrect coefficient of \(x^2\). Exam tip: take the square roots of the first and last terms and verify the middle term using \(2ab\).
Frequently asked questions
What is the correct answer to this question?
\((7x-3)^2=0\)
Why is this the correct answer?
Using \((a-b)^2=a^2-2ab+b^2\), we get \((7x-3)^2=49x^2-42x+9\). Hence the equation becomes \((7x-3)^2=0\). In option B, the middle term would be \(+42x\), while options C and D have an incorrect coefficient of \(x^2\). Exam tip: take the square roots of the first and last terms and verify the middle term using \(2ab\).
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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