If one root of x² + ax + 12 = 0 is 3, what are the other root and a?
Answer and explanation
Correct answer: Other root 4, a = −7
Let the roots be 3 and r. For x² + ax + 12 = 0, Vieta’s product relation gives 3r = 12, so r = 4. The sum of the roots is 3 + 4 = 7. Vieta’s sum relation says the sum equals −a because the coefficient of x² is 1; hence −a = 7 and a = −7. Therefore option A is correct. It can also be verified directly by substituting x = 3: 9 + 3a + 12 = 0 gives 3a = −21 and a = −7. The other options either use an incorrect sign or fail to satisfy the constant term and the given root simultaneously.
Frequently asked questions
What is the correct answer to this question?
Other root 4, a = −7
Why is this the correct answer?
Let the roots be 3 and r. For x² + ax + 12 = 0, Vieta’s product relation gives 3r = 12, so r = 4. The sum of the roots is 3 + 4 = 7. Vieta’s sum relation says the sum equals −a because the coefficient of x² is 1; hence −a = 7 and a = −7. Therefore option A is correct. It can also be verified directly by substituting x = 3: 9 + 3a + 12 = 0 gives 3a = −21 and a = −7. The other options either use an incorrect sign or fail to satisfy the constant term and the given root simultaneously.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
