Question

if alpha and beta are zeroes of the polynomial f(x)=x^2+2x-8, α^4+β^4=

Answer 1

your answer is in the above attachment

Answer 2

Answer:

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

Step-by-step explanation:

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