Linear Quadratic Answers

Quadratic Equation - CAT 2007 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 co-efficient 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?

1. -22.5
2. 16
3. -10.5
4. -17.5

Correct Answer is -17.5. Correct Choice is (4)

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Explanatory Answer

We know that the product of the roots of a quadratic equation ax² + bx + c = 0 isc/a

In the given equation, x² + mx + 24 = 0, the product of the roots =24/1 = 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 =24/15= 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-b/a  =  -m /1 = -m
Sum of the roots = 16 + 1. 5 = 17 = -17.5.
Therefore, the value of m = -17.5