Question

Find a degree 3 polynomial that has zeros -3,3, and 5 and in which the coefficient of x^2 is -10.The polynomial is: _____

Answer 1

Given the polynomial has zeros = -3, 3, 5

so, the factors are:

`(x+3),(x-3),(x-5)`

Multiplying the factors to find the equation of the polynomial:

So,

`\begin{gathered} y=(x-3)(x+3)(x-5) \\ y=(x^2-9)(x-5) \\ y=x^2(x-5)-9(x-5) \\ y=x^3-5x^2-9x+45 \end{gathered}`

But the coefficient of x^2 is -10.

So, Multiply all the coefficients by 2

So, the answer will be:

The polynomial is:

`2x^3-10x^2-18x+90`