Free Printable Test: (Solving Quadratic equations all methods)

1.

Solve by factoring:

Resolver por factorización

x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

2.

Solve by factoring:

Resolver por factorización

2x²+ 7x + 6 = 0

a)

x= 3/2 and x = 2

b)

x = -3/2 and x = -2

c)

x = 6 and x = 7

d)

x = -6 and x = -7

3.

Solve by factoring:

Resolver por factorización

3x² + 5x + 2 = 0

a)

x = -2/3 and x = -1

b)

x = -3/2 and x = -1

c)

x = 2/3 and x = 1

d)

x = 2/3 and x = -1

4.

Solve by factoring:

Resolver por factorización

4x² + 11x - 3 = 0

a)

x = -3/4 and x = -1

b)

x = 4 and x = 3

c)

x = 1/4 and x = -3

d)

x = -1/4 and x = 3

5.

Solve by factoring:

Resolver por factorización

5x² + 13x + 6 = 0

a)

x = -2 and x = -3/5

b)

x = 2 and x = 3/5

c)

x = -2 and x = 3/5

d)

x = 2 and x = -3/5

6.

Solve by Factoring

Resolver por factorización

7x² - 26x - 8 = 0

a)

x = -1 and x = -7/8

b)

x = 4 and x = -2/7

c)

x = -4 and x = 2/7

d)

x = 4 and x = -7/2

7.

Solve using the square root property

Resuelve usando la propiedad de la raíz cuadrada

16a² - 9 = 0

a)

a = ^-3/₄, ³/₄

b)

a = ^-4/₃, ⁴/₃

c)

a = ^-9/₁₆, ⁹/₁₆

d)

a = ^-16/₉, ¹⁶/₉

8.

Solve using the square root property

Resuelve usando la propiedad de la raíz cuadrada

$g^2+1=19$

a)

$g=\pm2\sqrt{5}$

b)

$g=\pm2\sqrt{3}$

c)

No solution

d)

$g=3\sqrt{2}$ and $g=-3\sqrt{2}$

9.

Solve using the square root property

Resuelve usando la propiedad de la raíz cuadrada

$x^2=-16$

a)

$\left\{\pm4\right\}$

b)

$\left\{0\right\}$

c)

$\left\{\pm4i\right\}$

d)

$\left\{4i\right\}$

10.

Solve using the square root property

Resuelve usando la propiedad de la raíz cuadrada

$4x^2-3=-51$

a)

$\left\{\pm2\sqrt{3}\right\}$

b)

$\left\{\pm2i\sqrt{3}\right\}$

c)

$\left\{2\sqrt{3}\right\}$

d)

$\left\{2i\sqrt{3}\right\}$

11.

Solve using the square root property

Resuelve usando la propiedad de la raíz cuadrada

$10\left(x-7\right)^2=440$

a)

$\left\{\pm2\sqrt{11}\right\}$

b)

$\left\{7\pm\sqrt{430}\right\}$

c)

$\left\{7\pm2\sqrt{11}\right\}$

d)

$\left\{\pm9\sqrt{11}\right\}$

12.

Solve using the square root property

Resuelve usando la propiedad de la raíz cuadrada

$2\left(x-2\right)^2+3=-37$

a)

$\left\{2\pm2\sqrt{5}\right\}$

b)

$\left\{\pm4i\sqrt{5}\right\}$

c)

$\left\{2\pm2i\sqrt{5}\right\}$

d)

$\left\{\pm2\sqrt{5}\right\}$

13.

Solve using the square root property

Resuelve usando la propiedad de la raíz cuadrada

4(x+9)²=24

a)

{-9+√6,-9-√6}

b)

{3,-3}

c)

{3}

d)

so solution

14.

Solve using the square root property

Resuelve usando la propiedad de la raíz cuadrada

2(x + 2)² - 16 = 80

a)

x = -2 ± √48

b)

x = ± 8√3

c)

x = -6√3, 2√3

d)

x = -2 ± 4√3

e)

x = ± 2√3

15.

Solve the following quadratics equation by completing the square...

Resuelva la siguiente ecuación cuadrática completando el cuadrado...

x² + 12x + 8= 0

a)

x = -6 ± 2√7

b)

x = 6 ± 2√7

c)

x = 28 ± √6

d)

x = -28 ± √6

16.

Solve the following quadratics equation by completing the square...

Resuelva la siguiente ecuación cuadrática completando el cuadrado...

x²+ 6x - 4 = 36

a)

x = -7, 7

b)

x = 4, -10

c)

x = -4 +- √7

d)

x = 10, -4

17.

Solve the following quadratics equation by completing the square...

Resuelva la siguiente ecuación cuadrática completando el cuadrado...

$v^2+2v-23=0$

a)

$\left\{9,1\right\}$

b)

$\left\{-2,-12\right\}$

c)

$\left\{-2+3\sqrt{3},-2-3\sqrt{3}\right\}$

d)

$\left\{-1+2\sqrt{6},\ -1-2\sqrt{6}\right\}$

18.

Solve the following quadratics equation by completing the square...

Resuelva la siguiente ecuación cuadrática completando el cuadrado...

x² +12x = 5

a)

X = 6 + √41 or 6 − √41

b)

X= 35 or 47

c)

X = −6 + √41 or −6 − √41

d)

X = √35 or √47

19.

Solve the following quadratics equation by completing the square...

Resuelva la siguiente ecuación cuadrática completando el cuadrado...

$4x^2+5x+2=0$ .

a)

$x=\frac{5}{8}\pm\frac{\sqrt{7}}{8}$

b)

$x=\frac{-5\pm i\sqrt{7}}{8}$

c)

$x=-\frac{5}{8}\pm\frac{\sqrt{7}}{8}$

d)

$x=\frac{5\pm i\sqrt{7}}{8}$

20.

Which line contains a mathematical error when completing the square?

¿Qué línea contiene un error matemático al completar el cuadrado?

a)

Line 1

b)

Line 2

c)

Line 3

d)

Line 4

e)

There is no error

21.

Solve By Square Roots: Resolver por raíces cuadradas:

$9x^2+3=-1$

a)

$\pm\frac{2}{3}$

b)

$\pm\frac{4}{9}i_{ }$

c)

$\pm\frac{2}{3}i$

d)

$\pm\frac{4}{9}$

22.

Solve using the Quadratic Formula

Resuelve usando la fórmula cuadrática.

x² + 4x = 9

a)

-2 ± √13

b)

-2 ± 2√7

c)

-2 ± √7

d)

-2 + √7

23.

Solve using the Quadratic Formula

Resuelve usando la fórmula cuadrática.

2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

24.

Solve using the Quadratic Formula

Resuelve usando la fórmula cuadrática.

$9u^2-11u+7=0$

a)

$\frac{-11\pm\sqrt{131}}{18}$

b)

$\frac{11\pm i\sqrt{131}}{18}$

c)

$\frac{11\pm\sqrt{131}}{-18}$

d)

$\frac{11\pm i\sqrt{373}}{18}$

25.

Solve using the Quadratic Formula

Resuelve usando la fórmula cuadrática. $-12q^2+3q+7=0$

a)

$\frac{-3\pm\sqrt{345}}{24}$

b)

$\frac{3\pm\sqrt{345}}{-24}$

c)

$\frac{3\pm\sqrt{345}}{24}$

d)

$\frac{3\pm i\sqrt{39}}{24}$

26.

Solve using the Quadratic Formula

Resuelve usando la fórmula cuadrática. $18j^{2\ }+9j\ +16=12+7j^2$

a)

$\frac{-9\pm i\sqrt[\ \ \ ]{95}}{22}$

b)

$\frac{9\pm i\sqrt[\ \ \ ]{95}}{22}$

c)

$\frac{-3\pm i\sqrt[\ \ \ ]{95}}{11}$

d)

$\frac{3\pm i\sqrt[\ \ \ ]{95}}{11}$

27.

x⁴- 16

28.

x²- 225

29.

9x²- 49y⁶

30.

What is the factored form of 5n³-10n²+3n-6

31.

What is the factored form of x³+7x²-2x-14

32.

Simplify. Write your answer in standard form:
(3x³+9x²-2x)−(7x³-6x²+1)

a)

10x³+15x²-3x

b)

-4x³+3x²-2x+1

c)

-4x³+15x²-2x-1

d)

-4x³+15x²-2x+1

33.

Simplify the product. Write the answer in standard form.
(y+6)(6y²+9y-8)

34.

What is the factored form of 6d⁴+9d³-12d²

35.

What is the GCF of 8c³+12c²+10c

(a)

36.

Classify the following polynomial

a)

quartic polynomial

b)

quadratic polynomial

c)

quartic trinomial

d)

quadratic trinomial

37.

Classify the following polynomial

a)

Quintic Polynomial

b)

Quartic Polynomial

c)

polynomial

38.

What is the degree?
- 3x³ - x² - 10x + 12

(a)

39.

What is the degree?
(x-3)(x²+2x+7)

(a)

40.

Classify the following polynomial

a)

binomial polynomial

b)

quadratic binomial

c)

quartic binomial

41.

$(9xy^2z)^8$

42.

Simplify: $\frac{12x^5y^4}{4x^3y^7}$

43.

Simplify: $\frac{6x^{-2}y^3}{2x^5y^{-1}}$

44.

What is the value of g in the equation

(a)

45.

$\frac{1}{2}\left(1-x\right)=-1\left(\frac{3}{2}x+1\right)$

(a)

46.

Solve for n:

(a)

47.

Solve for x.

\frac{3}{4}\left(x-4\right)=-\frac{1}{4}\left(x-16\right)

(a)

48.

$Solve\ for\ x.\ \ \ \ \ \ \ \ \ \ \ \ \ 20\ =\ \frac{x\ +\ -8}{-5}$

(a)

49.

$\frac{m}{3}+\frac{5}{3}=\frac{3m-4}{3}$

What do you multiply each term by to remove the fraction?

(a)

50.

$Solve\ for\ y.\ \ \ \ \frac{2y\ -\ 5}{3}\ -\ 4\ =\ \frac{y\ +\ 2}{5}$

(a)

Test: (Solving Quadratic equations all methods)

Total questions: 50

Worksheet time: 56mins

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