Question

Alpha and Beta are zeroes of polynomial x²-5x+k such that alha-beta=1 Find value of k

Answer 1

Dear student,

let α and β are two zeros of given polynomial

Polynomial = x²-5x+k

also α-β = 1 (given)

So α = 1+β ______________(1)


We have a=1, b= -5 and c=k

we know product of zeros = c/a =k (in the equation )

k = αβ

k = (1+β )(β) ∵[α=1+β] from equation (1)


k = β+β²______________(2)

also, -b/a = sum of zeros = -(-5)/1 = 5

So,

5 = α+β

5 = β+1+β ∵[α=1+β] from equation (1)

5 = 2β+1

4 = 2β

β = 4/2=2

=> β =2


put value of β=2 in equation (2)
we get ,

k= β+β²

k= 2+2²

k= 2+ 4

k= 6 is the answer


hope you understood

Regards