Question

If alpha and beta are the zeros of the polynomial 3 x square - 5 x minus 2 find a value of alpha by beta and beta by alpha and alpha cube + beta cube

Answer 1

Step-by-step explanation:

Given -

• α and β are zeroes of polynomial p(x) = 3x² - 5x + 2

To Find -

• Value of α/β + β/α

And

• α³ + β³

Now,

→ 3x² - 5x - 2

→ 3x² - 3x - 2x + 2

→ 3x(x - 1) - 2(x - 1)

→ (x - 1)(3x - 2)

Zeroes are -

→ x - 1 = 0 and 3x - 2 = 0

→ x = 1 and x = 2/3

Now,

The value of α/β + β/α is

→ 2/3÷1 + 1 ÷ 2/3

→ 2/3 + 3/2

→ 4 + 9/6

→ 13/6

And

The value of α³ + β³ is

→ (1)³ + (2/3)³

→ 1 + 8/27

→ 27+8/27

→ 35/27

Hence,

The value of α/β + β/α is 13/6

And

The value of α³ + β³ is 35/27.