Solving Quadratic Equations by Quadratic Formula Worksheet

**Page 1**

1.

Which of the following are the solutions of the quadratic equation $\mathrm{ax}$^{2} + $\mathrm{bx}$ + $c$ = 0, when $a$ ≠ 0 and $b$^{2} - 4$\mathrm{ac}$ ≥ 0?

a. | $x$ = (-b ± √(b ^{2} - 4ac))/(2a) | ||

b. | $x$ = (-b ± √(b ^{2} - 4ac))/2 | ||

c. | $x$ = (b ± √(b ^{2} - 4ac))/(2a) | ||

d. | None of the above |

Correct answer : (1)

2.

Write the equation -$d$^{2} + 3 = 7$d$ - 6$d$^{2} in the standard form.

a. | 5$d$ ^{2} + 7$d$ + 3 = 0 | ||

b. | 5$d$ ^{2} - 7$d$ - 3 = 0 | ||

c. | 5$d$ ^{2} - 7$d$ + 3 = 0 | ||

d. | 5$d$ ^{2} + 7$d$ - 3 = 0 |

[Original equation.]

5

[Add 6

5

[Subtract 7

5

[Rewrite the equation in the standard form.]

Correct answer : (3)

3.

What are the values of $a$, $b$ and $c$ in the quadratic formula used to solve the equation 8$e$^{2} - 4 + $e$ = - $e$^{2} + 6$e$?

a. | $a$ = -9, $b$ = -5 and $c$ = -4 | ||

b. | $a$ = 9, $b$ = -5 and $c$ = 4 | ||

c. | $a$ = 9, $b$ = -5 and $c$ = -4 | ||

d. | None of the above |

[Original equation.]

9

[Add

9

[Subtract 6

9

[Rewrite the equation in the standard form.]

In the quadratic formula,

So,

Correct answer : (3)

4.

What are the values of $a$, $b$ and $c$ in the equation 2$f$^{2} - 7$f$ + 31 = 0, which is in the standard form?

a. | $a$ = 2, $b$ = -7 and $c$ = 31 | ||

b. | $a$ = 2, $b$ = 7 and $c$ = 31 | ||

c. | $a$ = -2, $b$ = -7 and $c$ = -31 | ||

d. | None of the above |

2

[Original equation.]

[Compare the original equation with the standard equation.]

Correct answer : (1)

5.

Write the equation $\frac{1}{2}$$g$^{2} - 1 = - $\frac{7}{8}$$g$ in the standard form.

a. | 4$g$ ^{2} - 7$g$ - 8 = 0 | ||

b. | 4$g$ ^{2} + 7$g$ - 8 = 0 | ||

c. | 4$g$ ^{2} + 7$g$ + 8 = 0 | ||

d. | 4$g$ ^{2} - 7$g$ + 8 = 0 |

[Original equation.]

[Add

4

[Multiply the equation by LCM, 8.]

4

[Rewrite the equation in the standard form.]

Correct answer : (2)

6.

Find the values of 7$j$ in the equation $\frac{1}{4}$ × $j$ ^{2} - 1 = $\frac{1}{2}$ × $j$ + 1.

a. | 28, -14 | ||

b. | -28, -14 | ||

c. | -28, 14 | ||

d. | 28, 14 |

[Original equation.]

[Subtract

[Subtract 1 from each side.]

[Multiply the equation with 4.]

[Rewrite the equation in the standard form as

[Solve for

7

[Substitute

Correct answer : (1)

7.

Solve the equation $\frac{1}{4}$$k$^{2} - 4$k$ + 12 = 0 by using the quadratic formula.

a. | $k$ = - 4, 12 | ||

b. | $k$ = 4, - 12 | ||

c. | $k$ = - 4, - 12 | ||

d. | $k$ = 4, 12 |

[Original equation.]

[Multiply the equation by 4.]

[Substitute

[Simplify inside the radical.]

[Write ± as two separate equations.]

[Simplify.]

Correct answer : (4)

8.

Find the solutions of the quadratic equation $p$^{2} + 8$p$ + 15 = 0.

a. | 3, 5 | ||

b. | - 3, 5 | ||

c. | 3, - 5 | ||

d. | - 3, - 5 |

[Original equation.]

[Substitute

[Simplify.]

[Simplify.]

[Simplify.]

Correct answer : (4)

9.

Write the equation ($\frac{4}{3}$× $h$^{2}) + 6 = $h$^{2} + ($\frac{16}{15}$× $h$) in the standard form and identify the values of $a$, $b$ and $c$.

a. | $a$ = 5, $b$ = 16 and $c$ = 90 | ||

b. | $a$ = 5, $b$ = -16 and $c$ = -90 | ||

c. | $a$ = 5, $b$ = -16 and $c$ = 90 | ||

d. | None of the above |

[Original equation.]

(

[Subtract

(

[Subtract (

5

[Multiply the equation with the LCM, 15.]

5

[Rewrite the equation in the standard form.]

[Compare the equation with the standard form,

Correct answer : (3)

10.

Find the value of $b$^{2} - 4$\mathrm{ac}$ for the equation -6$x$^{2} - 16$x$ - 8 = 0.

a. | -64 | ||

b. | 64 | ||

c. | 448 | ||

d. | None of the above |

[Original equation.]

6

[Rewrite the equation in the standard form.]

[Compare the equation with standard equation

[Substitute 6 for

= 64

[Simplify.]

Correct answer : (2)