If the sum of the roots of 2x² + mx + 8 = 0 is −3, what is m?
Answer and explanation
Correct answer: 6
For a quadratic equation ax² + bx + c = 0, the sum of its roots is −b/a. Comparing 2x² + mx + 8 = 0 with the standard form gives a = 2 and b = m. Hence the sum is −m/2. The question states that this sum equals −3, so −m/2 = −3. Multiplying both sides by 2 gives −m = −6, and therefore m = 6. Thus option A is correct. A common error is to use m/2 without the negative sign, which would lead to option B. The constant term 8 does not affect the sum of roots; it affects their product, which is c/a = 4.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
For a quadratic equation ax² + bx + c = 0, the sum of its roots is −b/a. Comparing 2x² + mx + 8 = 0 with the standard form gives a = 2 and b = m. Hence the sum is −m/2. The question states that this sum equals −3, so −m/2 = −3. Multiplying both sides by 2 gives −m = −6, and therefore m = 6. Thus option A is correct. A common error is to use m/2 without the negative sign, which would lead to option B. The constant term 8 does not affect the sum of roots; it affects their product, which is c/a = 4.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
