Question

if alpha and beta are the zeros of the quadratic polynomial FX equal to X square + X - 2, find the value of one upon Alpha minus one upon beta . kisi mai dam hai to pure step se solve karke dikha too mann jaunga​

Answer 1

Answer:

Step-by-step explanation:

f(x) = x² + x - 2

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

Let α and β be the zeroes of the polynomial.

sum of zeroes = α + β = -b/a = - 1/1 = 1

Product of zeroes = αβ = c/a = -2/1 = -2.

(α - β)² = (α + β)² - 4αβ

          = (-1)² - 4 (-2)

          =  1 + 8

          = 9

α - β = ±3

When  α - β = + 3,

1/α - 1/β = β - α / αβ = - (α - β) / αβ = - (+3)/ - 2 = 3/2

When  α - β = - 3,

1/α - 1/β = β - α / αβ = - (α - β) / αβ = -(-3) / - 2 = -3/2