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?

• A. -22.5
• B. 16
• C. -10.5
• D. -17.5

Answer 1

The correct option is D -17.5

We know that the product of the roots of a quadratic equation $a{x}^2+bx+c=0$ 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 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 is = -m
Sum of the roots = 16 + 1.5 = 17 = -17.5.
Therefore, the value of m = -17.5