NECO 2022 · Paper 1 · Q20

Quadratics & their graphs

Find the quadratic equation whose roots are 2 and $-3\frac{1}{2}$ .

Worked solution (try it first)

The roots give the factors $(x - 2)$ and $\left(x + \frac{7}{2}\right)$ .
Doubling the second gives $(2x + 7)$ .
Multiply out: $(x - 2)(2x + 7) = 2x^2 + 7x - 4x - 14$ .
So the equation is $2x^2 + 3x - 14 = 0$ , option D.

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