Question

for each of the following find a quadratic polynomial whose sum and product of zeros are given -8 /3 and 2 / 3 and also find the zeros of the polynomial by factorization method

Answer 1

$sum \: of \: zero \: = - \frac{b}{a} = - ( \frac{ 2}{3} ) = \frac{ - 2}{3} \\ product \: of \: zero = \frac{c}{a} = \frac{ - 8}{3} \\ 3 {x}^{2} - 2x - 8 \\ 3 {x}^{2} - 6x + 4x - 8 = 0 \\ 3x(x - 2) + 4(x - 2) = 0 \\ (x - 2)(3x + 4) = 0 \\ x - 2 = 0 \: \: \: \: 3x + 4 = 0 \\ x = 2 \: \: \: \: x = - \frac{4}{3}$