Question

If alpha and beta are the zeroes of the polynomial 6x2 + x - 2 find alpha square beta + alpha beta square

Answer 1

$heya \\ \\ \\ \alpha + \beta = - 1 \div 6 \\ \\ \\ and \\ \\ \\ \alpha \beta = - 1 \div 3 \\ \\ \\ \\ \alpha {}^{2} \beta + \alpha \beta {}^{2} = \alpha \beta ( \alpha + \beta ) \\ \\ \\ \\ \alpha {}^{2} \beta + \alpha \beta {}^{2} = ( - 1 \div 3) \times ( - 1 \div 6) \\ \\ \\ \alpha { \beta {}^{2} + \beta \alpha }^{2} = 1 \div 18$

Answer 2

6x²+ x- 2=0

BY FACTORIZATION:

6x²+4x- 3x-2=0

2x(3x+2)-1(3x+2)=0

(2x-1)(3x+2)=0

x= 1/2 0r x=-2/3

Hence, α=1/2 and β=-2/3

α²β+ αβ²= 1/2×1/2×-2/3+ 1/2×-2/3×-2/3

= -1/6+ 2/9

= 2/9