Question

find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficient x^-2x-8

Answer 1

${x}^{2} - 2x - 8 = 0 \\ {x}^{2} - 4x + 2x - 8 = 0 \\ x(x - 4) + 2(x - 4) = 0 \\ (x -4)(x + 2) = 0 \\ x = 4 \\ x = - 2$
relationship of zeroes x and y and coefficient
$x \times y = ( \frac{c}{a} ) \\ - 2 \times 4 = \frac{ - 8}{1} \\ - 8 = - 8 \\ x + y = \frac{ - b}{a} \\ - 2 + 4 = \frac{ - ( - 2)}{1} \\ 2 = 2$
hence relationship between coefficient and zeroes are proved.