Question

Find all zeros of the polynomial 2x^3 + 3x^2– 6x – 9 if two of its zeroes are √3 and. - √3

Answer 1

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Answer 2

Answer:

The given polynomial equation is ;

p(x) = 2x^3 + x^2 - 6x - 3 = 0 . The two zeros(roots) are given as ; sqrt(3) & -sqrt(3) . Let the third zero of p(x) be k, then from theory of equations, we must have ;

Sum of the roots = -1/2, that is

sqrt(3) - sqrt(3) + k = -1/2 ==> k = -1/2 .