Question

If α and β are the zeros of the quadratic polynomial f(x) = x² - 5x + 4 , find the value of (1/α) + (1/β) - 2αβ .

Answer 1

(1/α) + (1/β) - 2αβ = -27/4

Step-by-step explanation:

f(x) = x² - 5x + 4

α and β are the zeroes of the polynominial.

Then α + β = -b/a = 5

αβ = c/a  = 4

Now (1/α) + (1/β) - 2αβ = [α + β / αβ] - 2αβ = 5/4 - 8 = 5 - 32 / 4 = -27/4

(1/α) + (1/β) - 2αβ = -27/4

Answer 2

Answer:

(1/α) + (1/β) - 2αβ = -27/4  

f(x) = x² - 5x + 4

α and β are the zeroes of the polynominial.

Then α + β = -b/a = 5

αβ = c/a  = 4

Now (1/α) + (1/β) - 2αβ = [α + β / αβ] - 2αβ = 5/4 - 8 = 5 - 32 / 4 = -27/4

(1/α) + (1/β) - 2αβ = -27/4

Step-by-step explanation: