Free Printable Polynomial Equations and Rational Root Theorem

1.

Determine the number of real roots of the polynomial equation $x\left(x^2+36\right)\left(x^2+1\right)=0$ .

a)

0

b)

1

c)

4

d)

5

2.

Determine the number of real roots of the polynomial equation $-2x^2\left(3x-5\right)^2\left(x+6\right)=0$ .

a)

2

b)

3

c)

4

d)

5

3.

Determine the number of real roots of the polynomial equation $\left(x^2-8x-16\right)\left(x^2+5x+4\right)\left(x-1\right)^5=0$

a)

7

b)

8

c)

9

d)

10

4.

How many positive roots are there in the polynomial equation $x^4\left(x^2-9\right)\left(x+6\right)^3=0$ ?

a)

5

b)

3

c)

2

d)

1

5.

How many positive roots are there in the polynomial equation $\left(x^3-1\right)\left(x^2-5x+4\right)\left(x+3\right)=0$ ?

a)

3

b)

4

c)

5

d)

6

6.

How many negative roots are there in the polynomial equation

\left(x+8\right)^5\left(x-2\right)^3\left(2x+1\right)=0

?

a)

3

b)

4

c)

5

d)

6

7.

How many negative roots are there in the polynomial equation

\left(5x+3\right)\left(x-5\right)^2\left(4x-1\right)^4=0

?

a)

1

b)

4

c)

6

d)

7

8.

Find the number of rational roots of the polynomial equation $x^3\left(2x-7\right)^2\left(x+4\right)=0$ .

a)

1

b)

2

c)

5

d)

6

9.

Find the number of negative fractional roots of the polynomial equation $\left(x-2\right)^3\left(3x+1\right)^6\left(x-\frac{1}{2}\right)^4=0$ .

a)

6

b)

7

c)

8

d)

9

10.

Find the number of positive fractional roots of the polynomial equation $\left(5x-6\right)^2\left(2x+5\right)^3\left(x+7\right)^4=0$ .

a)

2

b)

4

c)

7

d)

9

11.

One of the roots of the polynomial equation $x^3-21x-20$ is -1. Find the other roots.

a)

4 and 5

b)

-4 and 5

c)

2 and 10

d)

-2 and 10

12.

The polynomial equation $x^3+6x^2-4x-24=0$ has exactly 3 rational roots and one of these is 2. Find the remaining roots.

a)

2 and 6

b)

-2 and -6

c)

3 and 4

d)

-3 and -4

13.

When the leading term of a polynomial equation is greater than 1, what can you say about the roots of the equation?

a)

All roots are irrational.

b)

All roots are fractions.

c)

Some roots are irrational.

d)

Some roots are fractions.

14.

All roots of a polynomial equation are real and rational.

a)

Always

b)

Sometimes

c)

Never

15.

How many possible factors of the constant term are there in the polynomial equation $x^3+4x^2-25x-28=0$ ?

a)

8

b)

10

c)

12

d)

14

16.

Is 6 a root of the polynomial equation $x^3+x^2-24x+36=0$ ?

a)

Yes

b)

No

17.

Is $\frac{1}{2}$ a root of the polynomial equation $2x^3+19x^2+32x-42=0$ ?

a)

Yes

b)

No

18.

Is -3 a root of the polynomial equation $3x^3+17x^2-62x-48=0$ ?

a)

Yes

b)

No

19.

The roots of a polynomial equation are $-\frac{2}{3},\ 1$ and $4$ . Give the equation.

a)

$3x^3+13x^2+2x-8=0$

b)

$3x^3-13x^2+2x+8=0$

c)

$3x^3+17x^2+22x+8=0$

d)

$3x^3-17x^2+22x-8=0$

20.

Given the rational roots of a polynomial equation which are 1, 4, and 10. Find the polynomial equation that satisfies the given roots.

a)

$x^3+15x^2+54x+40=0$

b)

$x^3-15x^2+54x-40=0$

c)

$x^3+15x^2-54x-40=0$

d)

$x^3-15x^2-54x+40=0$

Polynomial Equations and Rational Root Theorem

Total questions: 20

Worksheet time: 29mins

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