Question

QUESTION 14The polynomial function y = p(x) has roots at x = -3,x=2, and x = 5, and its y-intercept is y=-6. Write a formula (in factored form) for p(x)

Answer 1

From the roots of the eqution

`\begin{gathered} x=-3 \\ x=2 \\ x=5 \end{gathered}`

We have

`(x+3)(x-2)(x-5)`

So the form should be

`\begin{gathered} y=a(x+3)(x-2)(x-5)_{} \\ \\ \text{Where a is a constant } \end{gathered}`

Now, let's find a. From

`\begin{gathered} y=a(x+3)(x-2)(x-5) \\ \\ 3*-2*-5=30 \end{gathered}`

Since y = -6, we have that

`\begin{gathered} -6=30* a \\ -6=30a \\ a=(-6)/(30) \\ \\ a=-(1)/(5) \end{gathered}`

The formula for p(x) becomes

`y=-(1)/(5)(x+3)(x-2)(x-5)`