Question

find the zeros of 3x^2-x-4 and verify the relation brtween the zeros and coefficients

Answer 1

$3 {x}^{2} - x - 4 = 0 \\ 3 {x}^{2} - 4x + 3x - 4 = 0 \\ x(3x - 4) + 3x - 4 = 0 \\ (x + 1)(3x - 4) = 0 \\the \: \: zeros \: \: are \: \: x = - 1 \: \: or \: \: \frac{4}{3} \\ \\ sum \: \: of \: \: zeros = - 1 + \frac{4}{3} = \frac{1}{3} \\ from \: \: the \: \: polynomial \: \: sum = \frac{ - ( - 1)}{3} = \frac{1}{3} \\ \\ product \: \: of \: \: zeros = - 1 \times \frac{4}{3} = \frac{ - 4}{3} \\ from \: \: the \: \: polynomial \: \: product= \frac{ - 4}{3}$