Question

if alpha and beta are the zeroes of the polynomial 3x^2-x-2, then find the value of (i) alpha^2 beta + alpla beta ^2
​

Answer 1

Answer:

$\frac{2}{9}$

Step-by-step explanation:

Let $\alpha$ and $\beta$ bet the roots of the equation

$3x^2 - x - 2 = x^2 - \frac{x}{3} - \frac{2}{3} = 0$

so

$(x - \alpha) (x - \beta) = x^2 - (\alpha + \beta )x + \alpha \beta$

compare coefficients

$\alpha + \beta = \frac{-1}{3}$

$\alpha \beta = \frac{-2}{3}$

$\alpha^2 \beta + \alpha \beta^2 = \alpha \beta (\alpha + \beta ) = \frac{-1}{3} \frac{-2}{3} = \frac{2}{9}$