WAEC Further Mathematics 2023 Paper

The general form of a quadratic equation is:

$x^2$-(sum of roots) = 0

For equal roots it's:$x^2 - 2\alpha + \alpha^2 = 0$

$3x^2+px+12=0$

Divide through by 3

= $x^2 + \;\frac{p}{3}x + 4 = 0$

=$x^2 - \left(-\;\frac{p}{3}\right)x + 4 = 0$

$\text{So}, \alpha^2 = 4$

= α = √4 = ±2

Also,-$\;\frac{p}{3} = 2\alpha$

When α = 2

-$\;\frac{p}{3} = 2(2) = 4$

=p=-12

When α =-2

-$\;\frac{p}{3} = 2(-2) = -4$

= p = 12

∴ values of p = ±12