WAEC 2022 · Paper 1 · Q47

Quadratics & their graphs

If the equations $x^2 - 5x + 6 = 0$ and $x^2 + px + 6 = 0$ have common roots, find the value of $p$ .

Worked solution (try it first)

Factorise the first equation: $(x - 2)(x - 3) = 0$ , so the roots are 2 and 3.
For $x^2 + px + 6 = 0$ , the sum of the roots is $-p$ .
So $-p = 2 + 3 = 5$ .
So $p = -5$ , option D.

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