If α and β are roots of 6x² + 5x − 4 = 0, what is αβ?
Answer and explanation
Correct answer: −2/3
For a quadratic equation ax² + bx + c = 0 with roots α and β, Vieta’s product relation is αβ = c/a. In this equation, a = 6 and c = −4. Therefore αβ = −4/6 = −2/3, so option A is correct. The sign must be retained when using c; dropping the negative sign would incorrectly produce option B. The values −5/6 and 5/6 involve the coefficient b = 5 and therefore confuse the product formula with the sum formula, since α + β = −b/a = −5/6. Thus the constant and leading coefficients, not the middle coefficient alone, determine the product.
Frequently asked questions
What is the correct answer to this question?
−2/3
Why is this the correct answer?
For a quadratic equation ax² + bx + c = 0 with roots α and β, Vieta’s product relation is αβ = c/a. In this equation, a = 6 and c = −4. Therefore αβ = −4/6 = −2/3, so option A is correct. The sign must be retained when using c; dropping the negative sign would incorrectly produce option B. The values −5/6 and 5/6 involve the coefficient b = 5 and therefore confuse the product formula with the sum formula, since α + β = −b/a = −5/6. Thus the constant and leading coefficients, not the middle coefficient alone, determine the product.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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