Question

4. If and β are zeroes of the polynomial x²+4x+3, find the polynomial whose zeroes are 1+/ and 1+/ β

Answer 1

(1+β)/α = 2

(1+α)/β = 0

Explanation:

We need to determine the zeros of the polynomial. This would be done by equating the polynomial to zero and using factorization method to find the variables

x²+4x+3 = 0

x²+x+3x+3=0

x(x+1) +3 (x+1) = 0

(x+1)(x+3) = 0

(x+1)= 0 or (x+3) = 0

x= -1 or -3

If α = -1, and β=-3

(1+β)/α = (1-3)/-1 = -2/-1

(1+β)/α = 2

(1+α)/β = (1-1)/-3 =0/-3

(1+α)/β = 0