Question

if alpha and beta are the zeros of the quadratic polynomial f(x) =x^2 -5x+4 find the value of ( 1/alpha)+(1/ beta)-2 alpha beta

Answer 1

Answer :

The given quadratic polynomial is

f (x) = x² - 5x + 4

Since, α and β are the zeroes of f (x),

α + β = - (- 5)/1 = 5 ...(i)

and

αβ = 4/1 = 4 ...(ii)

Now,

1/α + 1/β - 2αβ

= (β + α)/(αβ) - 2αβ

= 5/4 - (2 × 4)

= 5/4 - 8

= (5 - 32)/4

= - 27/4

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