Question

If alpha and beta are the zeros of quadratic polynomial x2-2x-8 find the value of alpha4+beta4

Answer 1

Given:

α and β are zeroes of polynomial p(x) = x² - 2x - 8

To Find :

Find the value of α^4+ β^4

Solution:

→ x² - 2x - 8

→ x² + 2x - 4x - 8

→ x(x + 2) - 4(x + 2)

→ (x - 4)(x + 2)

Zeroes are -

→ x - 4 = 0 and x + 2 = 0

→ x = 4 and x = -2

Now, The value of α^4 + β^4 is

→ (4)^4 + (-2)^4

→ 256 + 16

→ 272

Hence,

The value of α^4 + β^4 is 272

Answer 2

$\large\underline\mathrm{Given:-}$

$\alpha \: and \: \beta \: are \: zeroes \: of \: poynomial \: (p) \: = x {}^{2} \: - 2x - 8 .$

$\large\underline\mathrm{To \: find}$

$Find \: the \: value \: of \: \alpha {}^{4} + \beta {}^{4}$

$\large\underline\mathrm{Solution}$

$\implies$ x² - 2x - 8

$\implies$ x² + 2x - 4x - 8

$\implies$ x(x + 2) - 4(x + 2)

$\implies$ (x - 4)(x + 2)

$\implies$ x = 4, -2

$The \: value \: of \: \alpha {}^{4} + \beta {}^{4} \: is$

$\implies$ (4)^4 + (-2)^4

$\implies$ 256 + 16

$\implies$ 272