GMAT Math Sample Question - Quadratic Equation
March 3, 2004
If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then what is the value of m?
| (A) | -22.5 |
| (B) | 16 |
| (C) | -10.5 |
| (D) | -17.5 |
| (E) | Cannot be determined |
Correct Answer (D) Choice (-17.5)
Solution:
We know that the product of the roots of a quadratic equation ax2 + bx + c = 0 is
In the given equation, x2 + mx + 24 = 0, the product of the roots = = 24.
The question states that one of the roots of this equation = 1.5.
If x1 and x2 are the roots of the given quadratic equation and let x 1 = 1.5.
Therefore, x 2 = = 16.
In the given equation, m is the co-efficient of the x term.
We know that the sum of the roots of the quadratic equation ax2 + bx + c = 0 is = -m
Sum of the roots = 16 + 1. 5 = 17 = -17.5.
Therefore, the value of m = -17.5
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