Algebra II : Quadratic Formula

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #321 : Quadratic Equations And Inequalities

Find the roots of .

Possible Answers:

no real solutions

Correct answer:

no real solutions

Explanation:

Use the quadratic equation: 

Since the original equation is in standard form,  where 

.

Therefore,

because the value of the discriminant (the component beneath the square root) is negative, this function has no real solutions.

Example Question #32 : Quadratic Formula

Solve .

Possible Answers:

No real solutions

Correct answer:

No real solutions

Explanation:

This function cannot be factor therefore, use the quadratic equation.

Since the original equation is in the form  where 

.

Therefore,

Since the value of the discriminant (the value beneath the square root symbol) is negative, this function has no real solutions.

 

Example Question #31 : Quadratic Formula

Solve .

Possible Answers:

Correct answer:

Explanation:

This particular function cannot be factored therefore, use the quadratic formula to solve.

Since the function is in the form  where 

the quadratic formula becomes as follows.

 

Example Question #34 : Quadratic Formula

Use the quadratic formula to solve for x:

Possible Answers:

Correct answer:

Explanation:

To solve this problem, you must first rewrite the equation into   form (quadratic form). 

After this you plug the numbers into the following quadratic equation:

Which upon doing  you get:

 

This simplifies to:

 

Example Question #31 : Quadratic Formula

Use the quadratic formula to find the roots of the quadratic, 

 

 

Possible Answers:

Correct answer:

Explanation:

 

Recall the general form of a quadratic, 

The solution set has the form, 

 

For our particular case, , and 

 

 

 

 

 

 

 

Example Question #36 : Quadratic Formula

Use the quadratic formula to find the roots of the following equation.

Possible Answers:

Correct answer:

Explanation:

First, simplify the equation, so that the numbers are easier to work with. We can see that we can factor a 2 from each term.

Now we can divide both sides by 2, to further simplify.

Now that we have simplified we can apply the quadratic formula. 

where a, b, and c are the constants defined as follows:

This means our a is 1, our b is -6, and our c is 8.

Finally, lets plug the numbers into the formula:

 and 

or more simply:

 

These are the roots of the equation.

Example Question #32 : Quadratic Formula

Find the roots of the equation using the quadratic equation.

Possible Answers:

Correct answer:

Explanation:

 

where a, b, and c are the constants defined as follows:

This means our a is 1, our b is -6, and our c is 8.

Finally, lets plug the numbers into the formula:

These are the roots of the equation.

 

Remember that using  is the exact same as writing:

Example Question #37 : Quadratic Formula

Use the quadratic formula to find the answer of the following quadratic equation.

Possible Answers:

Correct answer:

Explanation:

The quadratic equation is:

Therefore:

Which gives the answer:

 

Example Question #38 : Quadratic Formula

Solve for x:

Possible Answers:

Correct answer:

Explanation:

For a quadratic function 

the quadratic formula states that

Using the formula for our function, we get

Notice that we have a negative under the square root. This means that we must use the imaginary number 

and our roots will be imaginary.

Simplifying using i, we get

Example Question #39 : Quadratic Formula

Find the roots using the quadratic formula

Possible Answers:

Correct answer:

Explanation:

For this problem

a=1, the coefficient on the x^2 term

b=7, the coefficient on the x term

c=7, the constant term

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