Question

if one zero of polynomial f (x)=x2+px+8 is double the other ,then find the value of k and hence both zeroes of f (x).

Answer 1

$f(x) = {x }^{2} + px + 8 \\ \alpha + \beta = \alpha + 2 \alpha = \frac{ - p}{1} \\ 3 \alpha = - p \\ \alpha \times 2 \alpha = \frac{8}{1} \\ 2 { \alpha }^{2} = 8 \\ 2 { (\frac{ - p}{3}) }^{2} = 8 \\ \frac{2 {p}^{2} }{9} = 8 \\ {p}^{2} = 8 \times 9 \div 2 = 36 \\ p = + - 6 \\ \alpha = 2 \: or \: - 2 \\ \beta = 4 \: or \: - 4$

Answer 2

Answer:

zeroes are 2,4 and p = -6 or zeros are -2,-4 and p=6