Question

5x²-8x-4
find the zero of the polynomial and verify the relationship between the zeroes and the coefficients of the polynomial ​

Answer 1

Answer:

x = -2/5; x = 2

Step-by-step explanation:

$5 {x}^{2} - 8x - 4 = 0 \\ 5 {x}^{2} - 10x + 2x - 4 = 0 \\ 5x(x - 2) + 2(x - 2) = 0 \\ (5x + 2)(x - 2) = 0 \\ 5x + 2 = 0 \: \: \: x - 2 = 0 \\ x = - \frac{2}{5} \: \: \: \: \: x = 2$

relationship

$\alpha + \beta = - \frac{b}{a} = - ( \frac{ - 2}{5} + 2) = \frac{ 2 - 10}{5} = \frac{ - 8}{5} \\ \alpha \beta = \frac{c}{a} = \frac{ - 2}{5} \times 2 = \frac{ - 4}{5}$