Question

If α & β are the zeros of a polynomial p(x) = 3x2 -10x + 7 , find the value of α2 + β2.​

Answer 1

Answer:

Given,

• α & β are the zeros of a polynomial p(x) = 3x²-10x + 7

To find :—

• → α² + β²

Now,

$α + β = \frac{ - ( - 10)}{3}$

$\implies \: { \underline{\bold{α + β = \frac{10}{3} }}}$

And

${ \underline{ \bold{α β \: = \frac{7}{3} }}}$

Now,

${ \underline{ \bold{α^{2} + β^{2} = {(α + β)}^{2} - 2αβ}}}$

Substituting the values we get,

→

$α ^{2} + β ^{2} = {( \frac{10}{3} )}^{2} - 2 \times \frac{7}{3}$

$\implies \: α ^{2} + β ^{2} = \frac{100}{9} - \frac{14}{3}$

$\implies \: α ^{2} + β ^{2} = \frac{100 - 42}{9}$

$\implies \: \large { \boxed { \mathtt { \color{blue}{\bold{α ^{2} + β ^{2} = \frac{58}{9} }}}}}$

$\Large{\colorbox{yellow}{\underline{\underline{♠Answer♠:—\:\: α² + β²\: = 58/9} }}}$

Formula used :—

$\boxed {\bold{ {x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy}}$