Question

Write a polynomial of least degree with roots 1 and -9. un Write your answer using the variable x and in standard form with a leading coefficient of 1. ​

Answer 1

y = x² +8x -9

Explanation:

You want the least-degree polynomial with roots 1 and -9, written in standard form.

Factors

Each root p means there is a factor (x-p). The two roots make the factored form of the polynomial be ...

y = (x -1)(x +9)

Expanding this to standard form, we get ...

y = x² +8x -9

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Additional comment

A quadratic that has two roots, p and q, will have the standard form ...

y = (x -p)(x -q) = x² -(p+q)x +pq

That is, the linear term coefficient is the opposite of the sum of the roots, and the constant is their product. This means you can write down the equation directly from the roots:

y = x² -(1-9)x +(1)(-9) = x² +8x -9