Descartes' Rule of Signs 10/22/24

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

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

• It also has 5 negative real roots 

• It might also have 3 positive real roots instead

• It might also have 1 positive real root instead

• It might also have 3 negative real roots instead

• It might also have 1 negative real root instead

Find all the real zeros for the following function.

7. f(x) = x³ - 5x² - 29x -15; ​ ​

​ (a)   ​ (b)   ​ ​

• -3
• 4±√21
• 1
• ​-3±2√7
• -4
• 6
• 6±√39/3
• 3±3√5/2

Find all real zeros of the following function.

8. f(x) = x³ + 5x² -25x + 19; ​ (a)   ​​ (b)  

• 1
• -3±2√7
• 4±√21
• 6±√39/3
• 3±3√5/2
• -3
• -4
• 6

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

• 3 or 1 positive roots and 0 negative roots

• 4, 2, or 0 positive roots and 1 negative root

• 4, 2, or 0 positive roots and 0 negative roots

• 2 or 0 positive roots and 1 negative roots

How many positive solutions does the following polynomial have?

f(x) =3x⁵ - x⁴ + 3x² - 6x +11

• 4, 2, or 0

• 4

• 3 or 1

• 3

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

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

• 1 positive, 2 or 0 negative

• 1 positive, 1 negative

• 0 positive, 1 negative

• 1 positive, 0 negative