Descartes rule of signs and rational root theorem

What does Descartes' Rule of Signs determine?

• How many possible positive real solutions

• How many possible negative real solutions

• How many possible imaginary or complex solutions

 $x^5+3x^2-4x+120$  has how many total possible  negative real solutions?

• 4

• 3

• 2

• 1

• 5

 $x^5+3x^2+6x+70$  has how many total possible  negative real solutions?

• 4

• 3

• 2

• 1

• 5

 $x^5+3x^2-4x+120$  has how many total possible  positive real solutions?

• 4

• 3

• 2

• 1

• 0

When looking for possible negative roots, we need to look at...

• $f\left(x\right)$

• $f\left(-x\right)$

• $-f\left(x\right)$

• $x^n$ (highest power)

Tags

CCSS.HSF-IF.C.7C

 $f\left(-x\right)\ =\ x^4-3x+2$  

How many possible negative real roots?

(a)  

How many possible negatives real solutions does the following polynomial have?

f(x) = x⁴ - 3x³ - 17x² + 39x -20

• 3 or 1

• 3

• 1

• 2 or 0

Use Descartes Rule of Signs to determine the possible number of positive and negative real roots.

• 2 positive, 0 negative

• 1 positive, 1 negative

• 0 positive, 2 negative

• 0 positive, 0 negative

How many possible negatives solutions does the following polynomial have?

f(x) = x⁴ - 3x³ - 17x² + 39x -20

• 3 or 1

• 3

• 1

• 2 or 0

How many negative solutions does the following polynomial equation have?

6x⁵ - 2x⁴ + x² - 7x +1=0

• 1

• 4,2 or none

• 3 or 1

• 3