IXL - Descartes' Rule of Signs (Algebra 2 practice)

According to Descartes' Rule of Signs, can the polynomial function have exactly 2 positive real zeros, including any repeated zeros? Choose your answer based on the rule only.

(

)

–

yes

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Learn with an example

question

According to Descartes' Rule of Signs, can the polynomial function have exactly 1 positive real zero, including any repeated zeros? Choose your answer based on the rule only.

(

)

–

yes

key idea

Descartes' Rule of Signs

(

)

is a polynomial function with real coefficients and is written in descending order of degree:

The number of positive real zeros of
p
(
x
)
equals the number of sign changes of its coefficients, or is less than this by an even number.
The number of negative real zeros of
p
(
x
)
equals the number of sign changes of the coefficients of
p
(
–
x
)
,
or is less than this by an even number.

solution

Count how many times the coefficients of

(

)

change sign.

–

It can be helpful to use a table.

Write the terms of the polynomial in descending order of degree.

Terms	x 5	– 8 x 2	– 5 x	6
Coefficient	1	– 8	– 5	6
Sign of coefficient	+	–	–	+
Sign change?		yes	no	yes

The coefficients change sign twice. So,

(

)

can have 2 or 0 positive real zeros.

So, the answer is

no.

The polynomial function cannot have 1 positive real zero.

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