Question

Find the polynomial function with roots 1, -2, and 5

Answer 1

So, what s true about the roots of a polynomial function?

Answer 2

Since the roots are the values where the function equals zero, we could set up an equation to be

\[P(x) = (x - x_{1})(x-x_{2})(x-x_{3})\]
where \[x_{1} = 1, x_{2} = -2, and x_{3} = 5\]

Answer 3

So... P(x) = (x-1)(x+2)(x-5).

Then, we just do some multiplication...

\[(x-1)(x+2) = x^{2} + x - 2\]
\[(x^{2}+x-2)(x-5) = (x*x^{2} + x*x - 2*x - 5*x^{2} - 5*x + 10 \]
\[P(x) = x^{3}-4x^{2}-7x+10 \]