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You are here: Home » GMAT Problem Solving » Quadratic Equation » Question 2

The GMAT Sample Math Problem is from the topic Quadratic Equation.

If one of the roots of the quadratic equation x² + mx + 24 = 0 is 1.5, then what is the value of m?

1. -22.5
2. 16
3. -10.5
4. -17.5
5. Cannot be determined
   
   

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

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 x₁ = 1.5
Therefore, x₂ = = 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