WAEC 2023 · Paper 1 · Q36

If $m$ and $(m + 4)$ are the roots of $4x^2 - 4x - 15 = 0$ , find the equation whose roots are $2m$ and $(2m + 8)$ .

Worked solution (try it first)

The sum of the roots is $-\frac{b}{a} = 1$ , so $m + (m + 4) = 1$ and $m = -\frac{3}{2}$ .
The new roots are $2m = -3$ and $2m + 8 = 5$ .
Their sum is $2$ and their product is $-15$ .
The equation is $x^2 - (\text{sum})x + \text{product} = 0$ , which is $x^2 - 2x - 15 = 0$ , option D.