In which of the following perfect-square forms can the equation \(25x^2-20x+4=0\) be written?
Answer and explanation
Correct answer: \((5x-2)^2=0\)
Using the identity \(a^2-2ab+b^2=(a-b)^2\), we get \(25x^2-20x+4=(5x)^2-2(5x)(2)+2^2=(5x-2)^2\). Hence, the correct perfect-square form is \((5x-2)^2=0\). In option B, the middle term would be \(+20x\), while options C and D have incorrect leading terms, \(625x^2\) and \(x^2\), respectively. Exam tip: Always check the sign and coefficient of the middle term when applying a perfect-square identity.
Frequently asked questions
What is the correct answer to this question?
\((5x-2)^2=0\)
Why is this the correct answer?
Using the identity \(a^2-2ab+b^2=(a-b)^2\), we get \(25x^2-20x+4=(5x)^2-2(5x)(2)+2^2=(5x-2)^2\). Hence, the correct perfect-square form is \((5x-2)^2=0\). In option B, the middle term would be \(+20x\), while options C and D have incorrect leading terms, \(625x^2\) and \(x^2\), respectively. Exam tip: Always check the sign and coefficient of the middle term when applying a perfect-square identity.
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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