Question

if α and β are the zeros of the quadratic polynomial 2x2 + 5x + 2, then find the value of α^4 + β^4please answer fas​

Answer 1

Answer:

Explanation:

Given polynomial,

⇒ 2x² + 5x + 2

Finding it's zeros.

By quadratic formula :

$\longrightarrow \bf \dfrac{ - b \pm \sqrt{ {(b)}^{2} - 4ac} }{2a}$

On comapring the polynomial with the general form of quadratic equation i.e,. ax² + bx + c

We get,

• a = 2
• b = 5
• c = 2

Substituting the given values,

$= \dfrac{ - 5 \pm \sqrt{(5 {)}^{2} - 4(2)(2) } }{2(2)} \\ = \dfrac{ -5\pm \sqrt{25 - 16} }{4} \\ = \dfrac{-5 \pm \sqrt{9} }{4} \\ = \dfrac{-5 \pm 3}{4} \\ = \dfrac{-8}{4} \: { \rm \: or} \: \frac{ - 2}{4} \\ \sf \therefore\: \alpha = - 2 \: { \rm \: and} \: \beta = \frac{ - 1}{2}$

Finding the value of :

$\longrightarrow\sf { \alpha }^{4} + { \beta }^{4}$

$\sf \longrightarrow \: {(-2)}^{4} + \bigg( \dfrac{-1}{2}\bigg)^{4}$

$\sf \longrightarrow \: 16 + \dfrac{1}{16}$

$\sf \longrightarrow \: \dfrac{ 256+ 1}{16}$

$\sf \longrightarrow \: \dfrac{ 257}{16}$

${ \underline{ \sf \therefore{ { \alpha }^{4} + { \beta }^{4} = \dfrac{257}{16} }}}$