In which perfect-square form can 36x² − 60x + 25 = 0 be written?
Answer and explanation
Correct answer: (6x − 5)² = 0
Use the identity (p − q)² = p² − 2pq + q². Taking p=6x and q=5 gives (6x − 5)² = (6x)² − 2(6x)(5) + 5² = 36x² − 60x + 25. Therefore the equation 36x² − 60x + 25 = 0 is exactly equivalent to (6x − 5)² = 0, so option A is correct. The plus form would produce a positive middle term, 60x, not −60x. In option C, squaring 36x gives a leading term 1296x², and option D gives only x² as the leading term. The coefficients must therefore be matched before identifying the perfect-square identity.
Frequently asked questions
What is the correct answer to this question?
(6x − 5)² = 0
Why is this the correct answer?
Use the identity (p − q)² = p² − 2pq + q². Taking p=6x and q=5 gives (6x − 5)² = (6x)² − 2(6x)(5) + 5² = 36x² − 60x + 25. Therefore the equation 36x² − 60x + 25 = 0 is exactly equivalent to (6x − 5)² = 0, so option A is correct. The plus form would produce a positive middle term, 60x, not −60x. In option C, squaring 36x gives a leading term 1296x², and option D gives only x² as the leading term. The coefficients must therefore be matched before identifying the 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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