Question

24).If α and β are the zeroes of the quardratic polynomial f(x)=x²−x−4, find the value of 1/α+1/

β−α·β .​

Answer 1

Answer:

Since α,β are the zeroes of the polynomial, they are also the roots of the equation x

2

−5x+k=0

Sum of the roots =α+β=−b/a=5 →(I)

We know from the question that α−β=1 →(II)

(I)+(II)⇒2α=6

⇒α=3

⇒β=2 (by substituting for α in (I))

∴αβ=2×3=6 →(III)

Produuct of the roots =αβ=c/a=k→(IV)

∴k=6 (from (III),(IV))

Hence, the answer is option D.