Question

Find the zeroes of the polynomial xsquare - 2 x - 8. Also verify the relationship between the zeroes
coefficients of the polynomial.​

Answer 1

The given. a polynomial

${x}^{2} - 2x - 8 \\ {x }^{2} - (4 - 2)x - 8 \\ {x}^{2} - 4x + 2x - 8 \\ x(x - 4) + 2(x - 4) \\ (x - 4) (x + 2) \\ x - 4 = 0 \\ \alpha = 4 \\ x + 2 = 0 \\ \beta = - 2 \\ relation \: between \: zeroes \\ \alpha + \beta = \frac{ - b}{a} \\ 4 + ( - 2) = \frac{ - 2}{1} \\ 4 - 2 = - 2 \\ - 2 = - 2 \\ \alpha \beta = \frac{c}{a} \\ 4 \times ( - 2) = \frac{ - 8}{1} \\ - 8 = - 8$