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Quadratic Equation - March 3, 2004

The GMAT Sample Math question for the day is from the topic Quadratic Equation.

Question
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

The correct choice is (D) and the correct answer is -17.5.

Explanatory Answer
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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