In a visual model, the area of ((x+a)(x+b)) is (x^2+9x+20). What can be the values of (a) and (b)?
Answer and explanation
Correct answer: (4) and (5)
The governing identity is (x + a)(x + b) = x² + (a + b)x + ab. Comparing this general expansion with x² + 9x + 20 gives two conditions that must hold at the same time: a + b = 9 and ab = 20. The pair 4 and 5 satisfies both conditions because 4 + 5 = 9 and 4 × 5 = 20. Substitution verifies the result: (x + 4)(x + 5) = x² + 5x + 4x + 20 = x² + 9x + 20. Hence option A is correct. The pair 2 and 10 has the correct product but sum 12; 1 and 20 has sum 21; and 3 and 6 has sum 9 but product 18. Thus no other option matches both coefficients.
Frequently asked questions
What is the correct answer to this question?
(4) and (5)
Why is this the correct answer?
The governing identity is (x + a)(x + b) = x² + (a + b)x + ab. Comparing this general expansion with x² + 9x + 20 gives two conditions that must hold at the same time: a + b = 9 and ab = 20. The pair 4 and 5 satisfies both conditions because 4 + 5 = 9 and 4 × 5 = 20. Substitution verifies the result: (x + 4)(x + 5) = x² + 5x + 4x + 20 = x² + 9x + 20. Hence option A is correct. The pair 2 and 10 has the correct product but sum 12; 1 and 20 has sum 21; and 3 and 6 has sum 9 but product 18. Thus no other option matches both coefficients.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.
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