Question

Find the value of k if alpha and beta are zeroes of polynomial X square -5x+k and alpha and beta=-1

Answer 1

Let α and β are zeroes of the polynomial = x² - 5x + k .

On comparing with ax²+bx+c=0
a= 1, b= -5 , c = k

Sum of zeroes (α+β)= -b/a = 5/1
α+β= 5…………....(1)

Product of zeros(α.β)= c/a = k /1
= c/a = k …………(2)

given β=-1
thereforα.βe from (1)
α= 5-β = 5+1 = 6

from (2)
k = α.β = 6 * -1 = -6

hence the value of k = -6

hope the condition you have given is α = ? and β = -1
or else if you have given α = β = -1 , the question goes wrong and couldn't be solved