Question

If alpha + beta are tye zeros of the polynomial 2x²+3x-3 then the value of alpha square + beta square is?
Provide detailed explanation.​

Answer 1

Answer:

21/4

Step-by-step explanation:

Given that alpha + beta are the zeros of the polynomial 2x² + 3x - 3. Where a is 2, b is 3 and c is -3.

We need to find out the value of (alpha)² + (beta)².

Sum of zeros = -b/a

alpha + beta = -3/2 ----------- (1)

Product of zeros = c/a

alpha × beta = -3/2 ---------- (2)

Now,

(alpha)² + (beta)² = (alpha + beta)² - 2 × alpha × beta

Substitute the value of eq (1) & (2) in above formula,

→ (alpha)² + (beta)² = (-3/2)² - 2 × (-3/2)

→ (alpha)² + (betal² = 9/4 + 3

→ (alpha)² + (beta)² = (9 + 12)/4

→ (alpha)² + (beta)² = 21/4

Therefore, the value of (alpha)² + (beta)² is 21/4.