# High School Math : Finding Roots

## Example Questions

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### Example Question #44 : Quadratic Equations And Inequalities

Find the root(s) of the following quadratic polynomial.

Explanation:

We set the function equal to 0 and factor the equation. By FOIL, we can confirm that  is equivalent to the given function. Thus, the only zero comes from, and . Thus,  is the only root.

Explanation:

### Example Question #46 : Quadratic Equations And Inequalities

Solve the quadratic equation using any method:

Explanation:

Use the quadratic formula to solve:

### Example Question #47 : Quadratic Equations And Inequalities

Solve the following equation using the quadratic form:

Explanation:

Factor and solve:

or

This has no solutions.

Therefore there is only one solution:

### Example Question #48 : Quadratic Equations And Inequalities

Solve the following equation using the quadratic form:

Explanation:

Factor and solve:

or

Therefore the equation has four solutions:

### Example Question #49 : Quadratic Equations And Inequalities

Solve the following equation using the quadratic form:

Explanation:

Factor and solve:

or

Therefore the equation has two solutions.

### Example Question #50 : Quadratic Equations And Inequalities

Solve the following equation using the quadratic form:

Explanation:

Factor and solve:

Each of these factors gives solutions to the equation:

### Example Question #21 : Solving Quadratic Equations

The product of two consecutive positive numbers is .  What is the sum of the two numbers?

Explanation:

Let the first number and the second number.

The equation to sovle becomes , or .

Factoring we get , so the solution is .  The problem states that the numbers are positive, so the correct numbers are and , which sum to .

### Example Question #52 : Quadratic Equations And Inequalities

Two positive, consecutive odd numbers have a product of .  What is their sum?

Explanation:

Let first odd number and second odd number. Then:

Use the distributive property and subtract from both sides to get .

Factoring we get .

Solving we get , so .

The problem stated that the numbers were positive so the answer becomes .

### Example Question #53 : Quadratic Equations And Inequalities

Find the sum of the solutions to:

Explanation:

Multiply both sides of the equation by , to get

This can be factored into the form

So we must solve

and

to get the solutions.

The solutions are:

and their sum is   .

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