Question

if Alpha, beta are zeros of polynomial 2xsquare-6x+ k, find value of k. s.t
(Alpha+ beta) square - alpha × beta = 40​

Answer 1

${\huge{\underline{\underline{\sf {\mathfrak{Answer}}}}}}$

${\underline{\underline{\rm {Given:}}}}$

• $p(x)=2x^2-6x+k$
• $(\alpha + \beta )^2 -\alpha × \beta = 40$

${\underline{\underline{\rm {Solution:}}}}$

$\alpha + \beta = \dfrac{-Coefficient \ of \ x}{Coefficient \ of \ x^2}$

$\alpha + \beta = \dfrac{-(-6)}{2}$

$\alpha + \beta = 3$

$\alpha × \beta = \dfrac{Constant \ term }{Coefficient \ of \ x^2}$

$\alpha × \beta = \dfrac{k}{2}$

$\underline{\underline{\rm{Simplifying \ the \ given \ expreseion :}}}$

$\alpha + \beta )^2 - \alpha × \beta = 40$

$(3)^2 - \dfrac{k}{2} = 40$

$\dfrac{k}{2} = 9 - 40$

$\dfrac{k}{2} = -31$

$\boxed{\implies{\boxed{k = -62}}}$