In which perfect-square form can 16x² − 24x + 9 = 0 be written?
Answer and explanation
Correct answer: (4x − 3)² = 0
The governing identity is (p − q)² = p² − 2pq + q². Compare the expression with this pattern. The first term 16x² is (4x)², and the last term 9 is 3². The middle term produced by (4x − 3)² is −2(4x)(3) = −24x, exactly matching the given term. Therefore 16x² − 24x + 9 = (4x − 3)², so the equation becomes (4x − 3)² = 0 and option A is correct. Option B gives a positive middle term, while options C and D have incorrect leading terms and cannot expand to the original quadratic.
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What is the correct answer to this question?
(4x − 3)² = 0
Why is this the correct answer?
The governing identity is (p − q)² = p² − 2pq + q². Compare the expression with this pattern. The first term 16x² is (4x)², and the last term 9 is 3². The middle term produced by (4x − 3)² is −2(4x)(3) = −24x, exactly matching the given term. Therefore 16x² − 24x + 9 = (4x − 3)², so the equation becomes (4x − 3)² = 0 and option A is correct. Option B gives a positive middle term, while options C and D have incorrect leading terms and cannot expand to the original quadratic.
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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