Question

if a and b are th roots of x²+3x+2=0 then find a. 1/a² +1/b²​

Answer 1

Answer:

Step-by-step explanation:

a + b = $-b\a$/a

        = -3

ab = c/a

    = 2

1/a2 + 1/b2 = a2 + b2 / a2b2

                  = a2 + b2 + 2ab - 2ab / a2b2

                 = 9 + 4 - 4 / 4

                 = 9/4                  

Answer 2

Answer :

5/4

Explanation :

Given polynomial,

⇒ x² + 3x + 2 = 0

On comapring the polynomial with ax² + bx + c = 0 we get,

• a = 1
• b = 3
• c = 2

Then,

• α + β = -b/a = -3
• αβ = c/a = 2

Finding 1/α² + 1/β²

⇒ α² + β²/αβ

⇒ (α + β)² - 2αβ/(αβ)²

On substituting the given values,

⇒ [(-3)² - 2(2)]/(2)²

⇒ [9 - 4]/4

⇒ 5/4

Required answer : 5/4