IXL - Write a polynomial from its roots (Algebra 2 practice)

Write a polynomial of least degree with roots 0 and

–

Write your answer using the variable

and in standard form with a leading coefficient of 1.

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question

Write a polynomial of least degree with roots 0 and

–

Write your answer using the variable

and in standard form with a leading coefficient of 1.

key idea

The standard form of a polynomial of degree

(

)

is a polynomial and

is a real number such that

(

)

then

is called a zero or a root of

(

)

Factor Theorem

The binomial

(

–

)

is a linear factor of the polynomial

(

)

if and only if

is a zero (or root) of

(

)

Corollary to the Fundamental Theorem of Algebra

(

)

is a polynomial of degree

≥

with complex coefficients, then

(

)

has exactly

complex roots (including any repeated roots).

solution

Since there are 2 roots, the Corollary to the Fundamental Theorem of Algebra implies that the degree of the polynomial is at least 2. The problem requires that the polynomial is of least degree, so it must have degree 2.

Use the Factor Theorem to identify the factors. Then, multiply the factors.

Identify the factors.

Each root corresponds to one linear factor.

Since 0 is a root,

–

is a factor of the polynomial.

Since

–

is a root,

–

is a factor of the polynomial.

Multiply the factors.

(

)

So,

is a polynomial of least degree with roots 0 and

–

It is written in standard form with a leading coefficient of 1.

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Not feeling ready yet? These can help:

L.3Multiply polynomials

Q.2Find the roots of factored polynomials

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