If 2x^2+5x-3 is written with factors involving (x-alpha)(x-beta), what is alpha+beta?
Answer and explanation
Correct answer: -5/2
For a quadratic polynomial ax² + bx + c, the sum of its zeroes is given by alpha + beta = −b/a. Here a = 2 and b = 5, so alpha + beta = −5/2. Direct factorisation confirms this: 2x² + 5x − 3 = (2x − 1)(x + 3), whose zeroes are 1/2 and −3. Their sum is 1/2 − 3 = −5/2. Therefore option A is correct. The constant term −3 is related to the product of the zeroes, not their sum, so option C confuses the two coefficient relationships. Option B has the wrong sign, and option D does not represent either required relation. A leading nonzero constant in the factor form does not change the zeroes.
Frequently asked questions
What is the correct answer to this question?
-5/2
Why is this the correct answer?
For a quadratic polynomial ax² + bx + c, the sum of its zeroes is given by alpha + beta = −b/a. Here a = 2 and b = 5, so alpha + beta = −5/2. Direct factorisation confirms this: 2x² + 5x − 3 = (2x − 1)(x + 3), whose zeroes are 1/2 and −3. Their sum is 1/2 − 3 = −5/2. Therefore option A is correct. The constant term −3 is related to the product of the zeroes, not their sum, so option C confuses the two coefficient relationships. Option B has the wrong sign, and option D does not represent either required relation. A leading nonzero constant in the factor form does not change the zeroes.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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