Question

If x = 0 and x=-1 are the roots of the polynomial f(x) = 2x3 - 3x2 + ax +b, find
value of a and b​

Answer 1

g(x) = 2x^3 - 3x^2 + ax + b = 0

Since g(0) = 0 we know b = 0 . Factoring g gives us more information:

x(2x^2 - 3x + a) = 0 . Here, the factor “x” confirms that x = 0 is one of the roots

of g. The factor in parenthesis must also equal zero at the other roots and we know x = - 1 is a root. So we have:

2(- 1)^2 - 3(- 1) + a = 0 or 2 + 3 + a = 0 so a = - 5

With this new information we can finish factoring this cubic equation:

x(x + 1)(2x - 5) = 0 and now we see all three roots are 0, - 1, and 2.5