WAEC 2023 · Paper 1 · Q17

Polynomials & quadratic roots

If $3x^2 + px + 12 = 0$ has equal roots, find the values of $p$ .

Worked solution (try it first)

Equal roots means the discriminant is zero: $b^2 - 4ac = 0$ .
Put in $a = 3$ , $b = p$ , $c = 12$ : $p^2 - 4(3)(12) = 0$ , so $p^2 = 144$ .
So $p = \pm 12$ , option D.

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