In which of the following perfect-square forms can the equation \(9x^2-30x+25=0\) be written?
Answer and explanation
Correct answer: \((3x-5)^2=0\)
Use the identity \(a^2-2ab+b^2=(a-b)^2\). Here, \(9x^2=(3x)^2\), \(25=5^2\), and the middle term is \(-30x=-2\cdot3x\cdot5\). Therefore, \(9x^2-30x+25=(3x-5)^2\), so the equation becomes \((3x-5)^2=0\). Option B would produce a positive middle term. In exams, take the square roots of the first and last terms and verify the middle term using \(\pm2ab\).
Frequently asked questions
What is the correct answer to this question?
\((3x-5)^2=0\)
Why is this the correct answer?
Use the identity \(a^2-2ab+b^2=(a-b)^2\). Here, \(9x^2=(3x)^2\), \(25=5^2\), and the middle term is \(-30x=-2\cdot3x\cdot5\). Therefore, \(9x^2-30x+25=(3x-5)^2\), so the equation becomes \((3x-5)^2=0\). Option B would produce a positive middle term. In exams, take the square roots of the first and last terms and verify the middle term using \(\pm2ab\).
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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