Question

alpha and beta are the zeros of the quadratic polynomial 2x² + 5x + 2, then find the value of alpha^4 + beta^4​

Answer 1

Answer:

The value of α⁴ + β⁴ is 257/16.

Step-by-step explanation:

Given :

α and β are the zeros of the quadratic polynomial 2x² + 5x + 2

To find :

the value of α⁴ + β⁴

Solution :

First let's find the zeros of the given quadratic polynomial by splitting middle term.

 Let p(x) = 2x² + 5x + 2

p(x) = 0,

2x² + 5x + 2 = 0

2x² + 4x + x + 2 = 0

2x(x + 2) + 1(x + 2) = 0

(x + 2) (2x + 1) = 0

• (x + 2) = 0 ; x = -2
• (2x + 1) = 0 ; x = -1/2

The zeros of the quadratic polynomial are -2 and -1/2

Let

• α = -2

• β = -1/2

⇒ α⁴ + β⁴

⇒ (-2)⁴ + (-1/2)⁴

⇒ 16 + (1/16)

⇒ 257/16

Therefore, the value of α⁴ + β⁴ is 257/16

Answer 2

Answer:

answer will be 9l4

Step-by-step explanation:

you can refer to attached image

hope it helps

have a great day