Question

PLS answer this....​

Answer 1

Answer:

5/4

Step-by-step explanation:

Given polynomial is f(x) = x² - x - 2

Here, a = 1, b = -1, c = -2

α,β are the zeroes of the polynomial.

(i) Sum of zeroes:

α + β = -b/a

α + β = 1

(ii) Product of zeroes:

αβ = c/a

αβ = -2

Now,

Given: (1/α²) + (1/β²)

⇒ (α² + β²)/α²β²

⇒ [(α + β)² - 2αβ]/[αβ]²

⇒ [(1)² - 2(-2)]/(-2)²

⇒ [1 + 4]/4

⇒ 5/4

Hope it helps!

Answer 2

Solution:

The given Equation is f(x) = x² - x - 2

Here, a = 1 , b = -1 and c = - 2

• a and ß are Zeroes of this Quadratic Polynomial

Relationship Between Zeroes:

☞ Sum of Zeroes = -b/a

a + ß = -b/a

a + b = 1

☞ Product of Zeroes = c/a

aß = c/a

aß = -2

Now, We have to find the value of 1/a² + 1/ß²

☞ 1/a² + 1/ß²

☞ a² + ß² / a².ß²

☞ (a + ß)² - 2ab / (ab)(ab)

☞ (-1)² - 2.-2 / -2 × -2

☞ 1 + 4 / 4

☞ 5/4

Answer is 5/4