WAEC Mathematics 2021 Paper

Concept:For any quadratic equation with roots $\alpha$ and $\beta$, the standard form is $$x^2 - (\alpha + \beta)x + \alpha\beta = 0.$$Explanation:Here, the given roots are $\alpha = -2q$ and $\beta = 5q$.First, find the sum of the roots: $$\alpha + \beta = -2q + 5q = 3q.$$Next, find the product of the roots: $$\alpha\beta = (-2q)(5q) = -10q^2.$$Substitute these values into the standard quadratic equation formula: $$x^2 - (3q)x + (-10q^2) = 0.$$Simplify the expression to obtain the required quadratic equation: $$x^2 - 3qx - 10q^2 = 0.$$This matches the form given in one of the options.Answer:The quadratic equation is $$x^2 - 3qx - 10q^2 = 0,$$ which corresponds to option D.