Question

If α and β are the zeroes of the polynomial $x^{2}$ + 12x + 35; frame a quadratic polynomial whose zeroes are α/2 and β/2.

Answer 1

Explanation:

$p(x) = {x}^{2} + 12x + 35 \\ let \: a = 1 \: \: \: b = 12 \: \: \: c = 35 \\ now \\ \\ \frac{ \alpha }{2} + \frac{ \beta }{2} = \frac{( \alpha + \beta )}{2} = \frac{ \frac{ - b}{a} }{2} = - \frac{ \frac{ - 12}{1} }{2} = - 6$