This GMAT sample question is a math problem solving question from Quadratic Equations. Concept tested: Coefficients of quadratic expressions and their relation to the sum and product of roots of quadratic equations. A sub 600 level GMAT practice question in algebra.

Question 8: If one of the roots of the quadratic equation x^{2} + mx + 24 = 0 is 1.5, then what is the value of m?

- -22.5
- 16
- -10.5
- -17.5
- Cannot be determined

@ INR

The given quadratic equation is x^{2} + mx + 24 = 0

Substitute x = 1.5 in the above equation because 1.5 is a root of the equation.

(1.5)^{2} + 1.5m + 24 = 0

2.25 + 1.5m + 24 = 0

1.5m = -26.25 Or m = \\frac{-26.25}{1.5}) = -17.5

For quadratic equations of the form ax^{2} + bx + c = 0, whose roots are \\alpha) and \\beta),

Sum of the roots, \(\alpha + \beta)) = \-\frac {b} {a}), and product of the roots, \\alpha\beta) = \\frac {c} {a}).

From the question stem, we know that one of the roots is 1.5. Let \\alpha) be 1.5.

Product of the roots of the quadratic equation x^{2} + mx + 24 = 0 is \\frac {c} {a}) = \(\frac {24} {1})) = 24.

i.e., \\alpha * \beta) = 24 where \\alpha) is 1.5.

1.5 * \\beta) = 24

\\beta) = \(\frac {24} {1.5}))

\\beta) = 16

In the given equation, m is the co-efficient of the x term.

We know that the sum of the roots of quadratic equations of the form ax^{2} + bx + c = 0 is \\frac {-b} {a})=\\frac {-m} {1}) = -m

Sum of the roots = 16 + 1.5 = 17.5

Sum of the roots = -m

If –m = 17.5, the value of m = -17.5

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