Find a third degree polynomial function ith real coefficient
Find a third degree polynomial function ith real coefficients that has -3 and plus or minus 2
Solution
the third degree polynomial with zeros -3 , + 2,-2 are
p(x) = (x-a) (x-b) (x-c)
where, a,b,c are zeros of polynomial
p(x) = ( x-(-3)) (x-2)(x-(-2))
p(x) = (x+3)(x-2)(x+2)
p(x) = (x+3)(x^2-4) = x^3 -4x +3x^2 -12
therefore, third degree polynomial is
p(x) = x^3 +3x^2 -4x -12
