Free Printable Simplifying radicals and Quadratic Formula

1.

√48

a)

4√2

b)

6√3

c)

4√3

d)

4√2

2.

Simplify the following radical: √32

a)

3√2

b)

4√8

c)

16√2

d)

4√2

3.

√28

a)

7√2

b)

7√4

c)

4√7

d)

2√7

4.

√45

a)

3√5

b)

5√3

c)

9√5

d)

5√9

5.

Solve the equation for all real solutions in simplest form.
$8x^2+11x+7=6x^2$

a)

$-2\pm\sqrt{65}$

b)

$\frac{-2\pm\sqrt{65}}{4}$

c)

$\frac{-11\pm\sqrt{65}}{4}$

d)

$\frac{-11\pm\sqrt{77}}{4}$

e)

$\frac{-11\pm\sqrt{177}}{4}$

6.

Solve the equation for all real solutions in simplest form.
$5x^2+19x+11=2x$

a)

$\frac{-17\pm\sqrt{69}}{5}$

b)

$\frac{-17\pm\sqrt{69}}{10}$

c)

$\frac{-17\pm\sqrt{509}}{10}$

d)

$\frac{-11\pm\sqrt{69}}{10}$

e)

$\frac{-11\pm\sqrt{186}}{10}$

7.

Express the simplest radical form.
$\sqrt{90}$

a)

$10\sqrt{3}$

b)

$9\sqrt{10}$

c)

$3\sqrt{10}$

d)

$2\sqrt{45}$

e)

$5\sqrt{18}$

8.

Solve the equation for all real solutions in simplest form.
$-2x^2+4x+1=-6x^2$

a)

$\left\{-\frac{1}{2}\right\}$

b)

$\frac{-1\pm\sqrt{2}}{2}$

c)

$\left\{\frac{1}{2}\right\}$

d)

$\frac{5\pm\sqrt{27}}{2}$

e)

$\frac{10\pm\sqrt{92}}{-4}$

9.

What is $a$ in this quadratic equation

2x^2-14x+24=0

?

a)

2

b)

-2

c)

14

d)

24

10.

The quadratic equation can be used to solve quadratic equations that cannot be factored.

a)

True

b)

False

11.

Solve using the Quadratic Formula.

a)

A

b)

B

c)

C

d)

D

12.

If the discriminant is positive, then the solution will be

a)

one real solution

b)

two real solutions

c)

no real solutions

d)

one imaginary solution

13.

Determine the value of the discriminant and name the nature of the roots for the following:
x² + 7x + 13
Remember: b² - 4ac

a)

400, 2 real root

b)

0, 1 real root with a multiplicity of 2

c)

-400, 2 imaginary roots

d)

-3, 2 imaginary roots

14.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

15.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

16.

The discriminant is

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

17.

Solve using the quadratic formula...

9x² = 4 + 7x

a)

b)

c)

d)

No solution

18.

What are the solutions to following equation?

$2x^2-x+1=0$

a)

$\frac{1}{4}-\frac{\sqrt{5}}{4}\ and\ \frac{1}{4}+\frac{\sqrt{5}}{4}$

b)

$\frac{1}{4}-\frac{\sqrt{7}}{4}\ and\ \frac{1}{4}+\frac{\sqrt{7}}{4}$

c)

$\frac{1}{4}-\left(\frac{\sqrt{7}}{4}\right)i\ and\ \frac{1}{4}+\left(\frac{\sqrt{7}}{4}\right)i$

d)

$\frac{1}{4}-\left(\frac{\sqrt{5}}{4}\right)i\ and\ \frac{1}{4}+\left(\frac{\sqrt{5}}{4}\right)i$

Simplifying radicals and Quadratic Formula

Total questions: 18

Worksheet time: 2hrs 30mins

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