# Algebra II : Finding Roots

## Example Questions

### Example Question #51 : Solving Quadratic Equations

What are the roots of ?

Explanation:

To find the roots, or solutions, of this quadratic equation, first factor the equation.

When factored, it's

.

Then, set each of those expressions equal to 0 and solve for x.

.

### Example Question #52 : Solving Quadratic Equations

Find the roots of the equation

Explanation:

Pull out an  term

Two numbers are needed that add to  and multiply to be . Guess and check results in  and .

Each term must be set equal to 0 to find the roots.

The polynomial is degree 4 so there are 4 roots. To make the roots easier to find the expression can be written as

The roots are

### Example Question #53 : Solving Quadratic Equations

Find the roots for:

Explanation:

In order to find the roots, factorize the quadratic.

The multiple to the integer 52 are:

The last set can produce the middle term.

Write the binomials.

Setting the equation equal to zero, we have two equations:

Solving for the equations, we will have  as the possible roots.

### Example Question #54 : Solving Quadratic Equations

Which of the following is a possible root of ?

Explanation:

Use the quadratic equation to solve for the roots.

Substitute the values of the polynomial  into the equation.

Since we have a negative discriminant, we will have complex roots even though there are no real roots.

The roots are:

One of the possible roots given is:

### Example Question #55 : Solving Quadratic Equations

Find the roots of this quadratic equation:

This equation has complex roots.

None of these.

Explanation:

There are multiple methods to solve quadratics. Use whichever is easiest for the problem.

Solve by factoring:

What numbers will multiply to get  and what two numbers will multiply to get -14?

To solve for the roots, set the factors equal to 0 and solve:

### Example Question #56 : Solving Quadratic Equations

What are the roots of

Explanation:

To find the roots, or solutions, of this quadratic equation, first factor it.

Recall that when a function is in the  form, the factors of a and c when multiplied and added together must equal b.

First, identify factors of 6 that could equal -1. Y

ou have to think of your positive and negative signs here. Remember that  and you need to have one positive and one negative number to get -6.

Therefore, after factoring, you should get:

.

Then, set each of those expressions equal to 0.

.

### Example Question #57 : Solving Quadratic Equations

What are the roots of ?

Explanation:

Since this function is already factored and equal to 0, you can just set each expression equal to 0 to get your roots.

and

.

### Example Question #58 : Solving Quadratic Equations

Find a root for the parabolic function:

Explanation:

The equation will need to be simplified to its standard form.

Simplify this equation by using the FOIL method to expand .

Simplify the terms.

The equation becomes:

Distribute the negative two through the parentheses.

Combine like terms.

The equation in standard for becomes:

The standard form for a polynomial is:

Substitute the coefficients corresponding to the equation in standard form.

Simplify the radical.  The roots will be imaginary.

Simplify the fractions and replace  with .

### Example Question #59 : Solving Quadratic Equations

Find the roots for the quadratic equation

Explanation:

You can solve this quadratic in many different ways, including by graphing or using the quadratic formula. This particular quadratic can be factored:

we're looking for 2 numbers that add to 5 and multiply to

The numbers that work are 8 and -3:

continue factoring

The factors are and . Set each factor equal to zero:

### Example Question #60 : Solving Quadratic Equations

Find the roots of the quadratic equation