Question

Which quadratic equation has solutions x=8 and x=−1?

Answer 1

There are two ways you can do this

$Using the formula$


${x}^{2} - (sum \: of \: roots)x + poduct \: of \: roots = 0$

${x}^{2} - (8+-1)x + - 1 \times 8 = 0$


${x}^{2} - 7x - 8 = 0$


$Working backwards$


$x = 8 \: or \: x = - 1$
$\Rightarrow x-8=0 \: or \: x+1=0$

$\Rightarrow (x-8)(x + 1)=0$
$\Rightarrow {x}^{2} + x -8x - 8 = 0$
$\Rightarrow {x}^{2} - 7x - 8 = 0$