If one root of x² + ax + 40 = 0 is 5, what are the other root and a?
Answer and explanation
Correct answer: Other root 8, a = −13
Let the unknown root be s. Since the leading coefficient is 1, the product of the roots equals the constant term 40. Thus 5s = 40, so s = 8. The sum of the roots is −a, so 5 + 8 = 13 = −a, which gives a = −13. Substituting x = 5 confirms the equation: 25 − 65 + 40 = 0. Option C has the correct second root but the opposite sign for a. Options B and D do not satisfy the required product of the roots. Therefore option A is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
Other root 8, a = −13
Why is this the correct answer?
Let the unknown root be s. Since the leading coefficient is 1, the product of the roots equals the constant term 40. Thus 5s = 40, so s = 8. The sum of the roots is −a, so 5 + 8 = 13 = −a, which gives a = −13. Substituting x = 5 confirms the equation: 25 − 65 + 40 = 0. Option C has the correct second root but the opposite sign for a. Options B and D do not satisfy the required product of the roots. Therefore option A is the unique correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
