Solving Equations in Quadratic Form Worksheet

**Page 1**

1.

Find the solution of the equation $x$^{4} - 11$x$^{2} + 30 = 0.

a. | {- 6, 6, - 5, 5} | ||

b. | {- 2$\sqrt{6}$, 2$\sqrt{6}$, - 2$\sqrt{5}$, 2$\sqrt{5}$} | ||

c. | {- 3$\sqrt{6}$, 3$\sqrt{6}$, - 2$\sqrt{6}$, 2$\sqrt{6}$} | ||

d. | {- $\sqrt{6}$, $\sqrt{6}$, - $\sqrt{5}$, $\sqrt{5}$} |

Let

(

Therefore, the roots of

[Equate each term to zero.]

[Substitute

[6 and 5 are roots of the equation.]

[Square on both the sides.]

Therefore, the solution of the equation is {-

Correct answer : (4)

2.

The number of real solutions of the equation |$x$|^{2} - 3|$x$| + 2 = 0 is _____

a. | 4 | ||

b. | 1 | ||

c. | 2 | ||

d. | 3 |

Then

[Substitute

(

[Factor.]

Let

Then

[Substitute

(

[Factor.]

Hence there are 4 real solutions for the given equation.

Correct answer : (1)

3.

Solve the equation 2 $x$ + $\sqrt{x}-1$ = 0

a. | 4 | ||

b. | 1 and $\frac{1}{4}$ | ||

c. | $\frac{1}{4}$ | ||

d. | 1 |

[Bring all the terms to one side except

[Squaring the above equation on both sides.]

4

[Write in the form of an equation

(

[Factors.]

[Solve for

When

1 ≠ - 1

[Substitute the values in

[From step 7.]

When

[Check by substituting in

[Squaring on both sides.]

Hence

Correct answer : (3)

4.

The equation $x$^{2} + 143 = 43 has a solution in which set of numbers?

a. | Integers | ||

b. | Irrational numbers | ||

c. | Complex numbers | ||

d. | Natural numbers |

[Original quadratic equation.]

[Subtract 43 to each side of the equation.]

[Simplify.]

So, the equation

Correct answer : (3)

5.

Verify if the equation can be written in quadratic form.

8$z$ + 17$\sqrt{z}$ = 0

a. | No | ||

b. | Yes |

Recall that

8

So, the given equation can be written in quadratic form.

Correct answer : (2)

6.

Verify if the equation can be written in quadratic form.

$x$^{4} + 4$x$^{2} = 5

a. | No | ||

b. | Yes |

(

So, the given equation can be written in quadratic form.

Correct answer : (2)

7.

Solve: ($d$ + 2)($d$ - 3) = 5$d$ + 10

a. | - 2, 3 | ||

b. | 8, - 2 | ||

c. | - 8, - 2 | ||

d. | - 8, 2 |

[Multiply.]

[Group the like terms and simplify.]

(

[Factor.]

Therefore,

So, the solutions are 8, - 2.

Correct answer : (2)

8.

Solve: $n$ - 4$\sqrt{n}$ - 45 = 0

a. | 81, 25$i$ | ||

b. | 81, 25 | ||

c. | 9, - 5 | ||

d. | 81 |

(

[Rewrite in quadratic form.]

[Replace

(

[Factor.]

Therefore,

[Solve for

That is

[Replace

[Square each side of the equation.]

Ignore

So, the solution is 81.

Correct answer : (4)

9.

Solve: ($j$ + 8)^{2} - 11($j$ + 8) + 28 = 0

a. | 0, -2 | ||

b. | 0, 2 | ||

c. | 1, 4 | ||

d. | -1, -4 |

[Replace (

(

[Factor.]

Therefore,

[Solve for

That is

[Replace

[Simplify.]

So, the solutions are -1 and -4.

Correct answer : (4)

10.

Verify if the equation can be written in quadratic form. $\frac{5}{s-5}+\frac{5}{5-s}$ = 4

a. | Yes | ||

b. | No |

(

[Multiply throughout by the LCD (

(25 - 5

0 = 4 (-

- 4

So, the given equation can be written in quadratic form.

Correct answer : (1)