# GMAT Maths | GMAT Quadratic Equations

###### GMAT Sample Questions | Roots & Equation | Sum & Product of Roots

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 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

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##### Approach to solve this GMAT Quadratic Equations Question: If 1.5 is a root of the quadratic equation, substituting x = 1.5 in the equation will satisfy the equation.

The given quadratic equation is x2 + 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 = $$frac{-26.25}{1.5}$ = -17.5 ### Alternative Method ##### Step 1 of solving this GMAT Quadratic Equations Question: Sum and Product of Roots of Quadratic Equations Theory For quadratic equations of the form ax2 + bx + c = 0, whose roots are $\alpha$ and $\beta$, Sum of the roots, $$$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. ##### Step 2 of solving this GMAT Quadratic Equations Question: Compute the second root of the equation Product of the roots of the quadratic equation x2 + 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 ##### Step 3 of solving this GMAT Quadratic Equations Question: Compute the value of ‘m’ 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 ax2 + 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 ##### Choice D is the correct answer. ###### GMAT Online Course - QuantTry it free! Register in 2 easy steps and Start learning in 5 minutes! ###### Already have an Account? ###### GMAT Live Online Classes Next Batch Dec 3, 2020 ###### GMAT Coaching in Chennai Next Integrated$Online + Offline) Batch
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