WAEC Further Mathematics 2023 Paper

Concept:A quadratic equation has equal roots when its discriminant is zero.Using the discriminant condition is the fastest way to find $p$.Explanation:The given equation is $3x^2+px+12=0$.For a quadratic equation $ax^2+bx+c=0$, the discriminant is $D=b^2-4ac$.Here, $a=3$, $b=p$, and $c=12$.For equal roots, $D=0$.So, $p^2 - 4(3)(12) = 0$.This simplifies to $p^2 - 144 = 0$.Therefore, $p^2 = 144$.Taking the square root of both sides gives $p = \pm \sqrt{144}$.Thus, $p = \pm 12$.Answer:The values of $p$ are $\pm 12$, so the correct option is A.