# Algebra II : Quadratic Roots

## Example Questions

← Previous 1

### Example Question #1 : Quadratic Roots

Give the solution set of the equation .

Explanation:

Using the quadratic formula, with :

### Example Question #2 : Quadratic Roots

Give the solution set of the equation  .

Explanation:

Using the quadratic formula, with :

### Example Question #3 : Quadratic Roots

Write a quadratic equation in the form  with 2 and -10 as its roots.

Explanation:

Write in the form  where p and q are the roots.

Substitute in the roots:

Simplify:

Use FOIL and simplify to get

.

### Example Question #4 : Quadratic Roots

Find the roots of the following quadratic polynomial:

This quadratic has no real roots.

Explanation:

To find the roots of this equation, we need to find which values of  make the polynomial equal zero; we do this by factoring. Factoring is a lot of "guess and check" work, but we can figure some things out. If our binomials are in the form , we know  times  will be  and  times  will be . With that in mind, we can factor our polynomial to

To find the roots, we need to find the -values that make each of our binomials equal zero. For the first one it is , and for the second it is , so our roots are .

### Example Question #5 : Quadratic Roots

Write a quadratic equation in the form  that has  and  as its roots.

Explanation:

1. Write the equation in the form  where  and  are the given roots.

2. Simplify using FOIL method.

### Example Question #6 : Quadratic Roots

Give the solution set of the following equation:

Explanation:

Use the quadratic formula with  and :

### Example Question #7 : Quadratic Roots

Give the solution set of the following equation:

Explanation:

Use the quadratic formula with , and :

### Example Question #8 : Quadratic Roots

Let

Determine the value of x.

Explanation:

To solve for x we need to isolate x. We can do this by taking the square root of each side and then doing algebraic operations.

Now we need to separate our equation in two and solve for each x.

or

### Example Question #9 : Quadratic Roots

Solve for :

Explanation:

To solve this equation, you must first eliminate the exponent from the by taking the square root of both sides:

Since the square root of 36 could be either or , there must be 2 values of . So, solve for

and

to get solutions of .

### Example Question #10 : Quadratic Roots

Find the roots of

Explanation:

When we factor, we are looking for two number that multiply to the constant, , and add to the middle term, . Looking through the factors of , we can find those factors to be  and .

Thus, we have the factors:

.

To solve for the solutions, set each of these factors equal to zero.

Thus, we get , or .

Our second solution is, , or

← Previous 1