Quadratic Equation  CAT 2016 Math Preparation
Question 4 the day : March 2, 2004
The question for the day is a sample practice problem in quadratic equation. Helps understand concepts related to roots of a quadratic equation and the nature of the roots of the quadratic equation. The question for the day is on finding a missing coefficient from the topic quadratic equation..
Question
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
Correct Answer is 17.5. Correct Choice is (4)
Explanatory Answer
We know that the product of the roots of a quadratic equation ax ^{2} + bx + c = 0 is
In the given equation, x ^{2} + mx + 24 = 0, the product of the roots = = 24.
The question states that one of the roots of this equation = 1.5.
If x _{1} and x _{2} 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 coefficient of the x term.
We know that the sum of the roots of the quadratic equation ax ^{2} + 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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