If one root of x² + ax + 24 = 0 is 4, what are the other root and a?
Answer and explanation
Correct answer: Other root 6, a = −10
Let the second root be s. Since the equation is monic, the product of its roots equals the constant term: 4s = 24, so s = 6. The sum of the roots equals the negative of the coefficient of x, therefore 4 + 6 = 10 = −a, and a = −10. Verification is immediate: 4² + (−10)(4) + 24 = 16 − 40 + 24 = 0. Option C keeps the correct second root but reverses the sign of a. Options B and D fail the product condition. Hence option A gives both required values.
Frequently asked questions
What is the correct answer to this question?
Other root 6, a = −10
Why is this the correct answer?
Let the second root be s. Since the equation is monic, the product of its roots equals the constant term: 4s = 24, so s = 6. The sum of the roots equals the negative of the coefficient of x, therefore 4 + 6 = 10 = −a, and a = −10. Verification is immediate: 4² + (−10)(4) + 24 = 16 − 40 + 24 = 0. Option C keeps the correct second root but reverses the sign of a. Options B and D fail the product condition. Hence option A gives both required values.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
