What POLYNOMIAL has the solutions of 2, -1, and 3 ???? 10 POINTS to best explanation<<<<<<<<<<<<<<<<<<<<<<

Question

How do i do this?

What polynomial has the solutions of 2, -1, and 3?

and what one has the solutions of -2, 3i?

thanks

Answer 1

Multiply it out:
(x-2)(x+1)(x-3)
= x^3 + (-2+1-3)4x^2 + (-2*1 + 1*-3 + -3*-2)x + -2*1*-3
= x^3 + 4x^2 + x + 6

Similarly:
(x+2)(x-3i)
= x^2 + (2-3i)x - 6i

Answer 2

If a polynomial has a solution x=c, then one factor of the polynomial is x-c. So in question 1, the factors are x-2, x+1 and x-3. Just multiply these together to get the cubic.

If a polynomial has one imaginary solution, it must have a conjugate imaginary solution. So, from above, the roots are x+2, x-3i and x+3i.