Question

If p and q are the roots of $2x^2+3x+4$ = 0, then find the value of $p^{2}q+q^{2}p$

Answer 1

For a quadratic equation given by $a{x}^2+bx+c$ = 0,
the sum of the roots = -$\frac{b}{a}$,
the product of the roots = $\frac{c}{a}$.

Given, quadratic equation: $2x^2+3x+4$ = 0,
here, a = 2, b = 3, c = 4

Here, p+q = sum of the roots = -$\frac{b}{a}$ = -$\frac{3}{2}$
Here, pq = product of the roots = $\frac{c}{a}$ = $\frac{4}{2}$ = 2.

$p^{2}q+q^{2}p$ = $pq(p+q)$ = -$\frac{3}{2}$$\times$2 = -3.