If one of the roots of the quadratic equation x2+ mx + 24 = 0 is 1.5, ...
Approach to solve: 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 = −26.251.5−26.251.5 = -17.5
Alternative Method
Step 1: Sum and Product of Roots of Quadratic Equations Theory
For quadratic equations of the form ax
2 + bx + c = 0, whose roots are α and β,
Sum of the roots, α + β =
, and product of the roots, αβ = c/a.
From the question stem, we know that one of the roots is 1.5. Let α be 1.5.
Step 2: Compute the second root of the equation
Product of the roots of the quadratic equation x2 + mx + 24 = 0 is c/a = (24/1) = 24.
i.e., α * β = 24 where α is 1.5.
1.5 * β = 24
β = (24/1.5)
β = 16
Step 3: 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 −b/a = −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.