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

Find a third degree polynomial function ith real coefficients that has -3 and plus or minus 2Solutionthe third degree polynomial with zeros -3 , + 2,-2 are p(x)

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