Question

for what values of k, -4 is a zeroes of the polynomial x^2-x-(2k+2) ?

Answer 1

(1)Given polynomial,
x²-x-(2k+2)
x²-x-(2k+2)=0
-4 is a zero of the polynomial
put x=-4,
(-4)²-(-4)-(2k+2)=0
16+4-(2k+2)=0
16+4-2k-2=0
20-2-2k=0
18-2k=0
2k=18
k=18/2
k=9

(2) α+β=-6
αβ=-4
The polynomial is
x²-x( α+β )+ αβ
x²-x(-6)+(-4)
x²+6x-4

So,the required polynomial is x²+6x-4

hope it helps