Question

if
$\alpha \: and \: \beta \: are \: the \: zeroes \: of \: polynomial \: 3x ^{2} - \: 2x - 6 \: then \: find \: ( \alpha + \beta ) ^{2} - 3 \alpha \beta$
​

Answer 1

alpha+beta=-b/a=2/3

alphabeta=c/a= -2

hence ans is 29/3

Answer 2

Answer:

$\frac{58}{9}$

Step-by-step explanation:

In the polynomial $3x^{2} -2x-6$

$\alpha + \beta = \frac{-b}{a}$

$\alpha\cdot\beta = \frac{c}{a}$

And,

$\frac{-b}{a} = -\frac{-2}{3} = \frac{2}{3}$

and $\frac{c}{a} =\frac{-6}{3}=-2$

So now in the expression - $(\alpha+\beta)^2-3\alpha\beta$

$\alpha+\beta = \frac{2}{3} \; and \; \alpha\beta=-2$

Inserting the values in the expression -

$(\frac{2}{3})^2-3(-2)$

= $\frac{4}{9} + 6$

= $\frac{58}{9} \;\;\;\;\;Ans$