Higher degree equations and inequalities

Roots of Polynomial Equation

Submitted by michaela.bailova on Wed, 04/17/2024 - 17:53

Submitted by michaela.bailova on Fri, 04/05/2024 - 12:57

Level:

Find the factored form of the equation.

x^{4} - 81 = 0

(x^{2} + 9) (x - 3) (x + 3) = 0

{(x - 3)}^{2} {(x + 3)}^{2} = 0

{(x - 3)}^{4} = 0

(x + 9) (x - 3) (x + 3) = 0

Level:

Find the sum of all the natural roots of the next equation. Multiple roots, if any, count only once.

(x^{3} + 8) (x^{2} - 1) = 0

1

- 1

3

0

Level:

Find the sum of all the natural roots of the next equation. Multiple roots, if any, count only once.

(x^{2} + 1) (x^{2} - 16) = 0

4

3

5

0

Level:

Find the sum of all real solutions of the following equation.

(2 - x) (x^{2} - 9) = 0

2

0

5

3

Level:

In the following list identify a true statement on the function

f

f (x) = (x + 3) (x - 1) (x - 2)

f (x) > 0 ⟺ x \in (- 3; 1) \cup (2; \infty)

f (x) > 0 ⟺ x \in (- 2; - 1) \cup (3; \infty)

f (x) > 0 ⟺ x \in (- \infty; - 3) \cup (1; 2)

f (x) < 0 ⟺ x \in (- 3; 1) \cup (2; \infty)

Level:

Assuming

x \in N

, find the solution set of the following equation.

3 x^{3} - 2 x^{2} = 0

\emptyset

{0}

{\frac{2}{3}}

{0; \frac{2}{3}}

Level:

Assuming

x \in N

, find the solution set of the following equation.

x^{3} - 8 x^{2} + 16 x = 0

{4}

\emptyset

{0; 4}

{- 4; 4}

Level:

Find the solution set of the inequality.

(4 - x^{2}) (x^{3} + 1) > 0

(- \infty; - 2) \cup (- 1; 2)

(- \infty; - 2)

(- \infty; 2)

(- \infty; - 1) \cup (0; 2)