Question

if alpha and beta are zeros of the polynomial 2 X square + 6 x minus 3 then find the value of the expression Alpha cube plus b cube

Answer 1

The answer is given in the attachment :

Answer 2

Answer:

$\alpha^{3}+\beta^{3}=\frac{-81}{2}$

Step-by-step explanation:

$Given \: \alpha \: and\: \beta \\ are \: zeroes \: of \:the \\polynomial \:2x^{2}+6x-3$

/* Compare above equation with ax²+bx+c,we get

a= 2, b = 6 , c = -3,

$i) Sum \: of \: the \: zeroes \\=\frac{-b}{a}$

$\implies \alpha+\beta=\frac{-6}{2}\\=-3\:---(1)$

$ii) Product\:of\:the\: zeroes\\=\frac{c}{a}$

$\implies \alpha+\beta=\frac{-3}{2}\:---(2)$

$Now,\:\alpha^{3}+\beta^{3}\\=\left(\alpha+\beta\right)^{3}-3\alpha\beta(\alpha+\beta)\\=\left(-3\right)^{3}-3\times \frac{-3}{2}\times (-3)$

$=-27-\frac{27}{2}\\=\frac{-54-27}{2}\\=\frac{-81}{2}$

Therefore,

$\alpha^{3}+\beta^{3}=\frac{-81}{2}$

•••♪