Question

if Alpha and beta are zereos of the quadratic polynomial x^2-6x+8, then find the value of Alpha - beta (Alpha>Beta)​

Answer 1

$if \: \alpha \: and \: \beta \: are \: zeros \: of \: the \: polynomial \: {x}^{2} - 6x + 8$

then we know that

$\alpha + \beta = 6$

and

$\alpha \beta = 8$

then

${ (\alpha - \beta )}^{2} = { \alpha }^{2} + { \beta }^{2} - 2 \alpha \beta$

that will be equal to

${ (\alpha - \beta) }^{2} = { (\alpha + \beta )}^{2} - 4 \alpha \beta$

by this

we get

${ (\alpha - \beta) }^{2} = {6}^{2} - 32 = 4$

${ (\alpha - \beta) } = + 2 \: or \: - 2$