Question

3. If one of the zeroes of the polynomial x^2+( k^2 - 2k)X +(k^4 - 3k^2+5k -1) is additive
inverse of the other then what will be the value of k?
(2 Points)​

Answer 1

Answer:

Step-by-step explanation:

let the zeros of the polynomial is a and the other is -a

p(x)=x^2+(k^2-2k)x+(k^4-3k^2+5k-1)

p(a)=0

a^2+(k^2-2k)a+(k^4-3k^2+5k-1)=0

a^2+k^2a-2ak+k^4-3k^2+5k-1=0---(1)

p(-a)=0

(-a)^2+(k^2-2k)(-a)+(k^4-3k^2+5k-1)=0

a^2-ak^2+2ak+k^4-3k^2+5k-1=0---(2)

(1)-(2)

2ak^2-4ak=0

2ak(k-2)=0

2ak=0

ak=0

k=0

k-2=0

k=2

the values of k will be 0,2