High School Math : Solving Quadratic Equations

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #44 : Quadratic Equations And Inequalities

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

Possible Answers:

Correct answer:

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. 

Example Question #45 : Quadratic Equations And Inequalities

Possible Answers:

Correct answer:

Explanation:

Example Question #71 : Intermediate Single Variable Algebra

Solve the quadratic equation using any method:

Possible Answers:

Correct answer:

Explanation:

Use the quadratic formula to solve:

Example Question #321 : Algebra Ii

Solve the following equation using the quadratic form:

Possible Answers:

Correct answer:

Explanation:

Factor and solve:

or

This has no solutions.

Therefore there is only one solution:

Example Question #81 : Intermediate Single Variable Algebra

Solve the following equation using the quadratic form:

Possible Answers:

Correct answer:

Explanation:

Factor and solve:

or

Therefore the equation has four solutions:

Example Question #81 : Intermediate Single Variable Algebra

Solve the following equation using the quadratic form:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

Explanation:

Factor and solve:

Each of these factors gives solutions to the equation:

Example Question #332 : Algebra Ii

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

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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:

 

Possible Answers:

Correct answer:

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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