Question

if alpha and beta are the zeros of the polynomial 3 x square - 5 x minus 2 find a value of Alpha Cube + beta cube

Answer 1

Answer:

Step-by-step explanation:

It will help you. Refer the attachment.

Answer 2

Answer:

$(\alpha)^{3}+(\beta)^{3}=\frac{215}{27}$

Step-by-step explanation:

$Given \:\alpha \:and\:\beta \:are\\zeroes \:of \:the \: polynomial \\3x^{2}-5x-2$

Compare this with ax²+bx+c , we get

a = 3, b = -5, c = -2,

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

$\implies \alpha+\beta = \frac{-(-5)}{3}\\=\frac{5}{3}\:---(1)$

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

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

$iii) (\alpha)^{3}+(\beta)^{3}\\=(\alpha+\beta)^{3}-3\alpha \beta(\alpha+\beta)\\=\left(\frac{5}{3}\right)^{3}-3\times \left(\frac{-2}{3}\right)\times \left(\frac{5}{3}\right)\\=\frac{125}{27}+2\times \frac{5}{3}\\=\frac{125}{27}+\frac{10}{3}\\=\frac{125+90}{27}\\=\frac{215}{27}$

Therefore,

$(\alpha)^{3}+(\beta)^{3}=\frac{215}{27}$

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