Algebra II : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #281 : Intermediate Single Variable Algebra

Determine the discriminant of the quadratic:  

Possible Answers:

Correct answer:

Explanation:

The quadratic function is in the form of .

The discriminant is the term inside the square root of the quadratic function defined as:  

Identify the coefficients.

Substitute the values into the equation.

The answer is:  

Example Question #1418 : Algebra Ii

Determine the discriminant of the following polynomial:  

Possible Answers:

Correct answer:

Explanation:

Reorder the equation in  standard format.

The discriminant is the term inside the square root of the quadratic equation.

Identify and substitute the coefficients for each term of the polynomial in standard form.

The answer is:  

Example Question #1421 : Algebra Ii

Determine the discriminant:  

Possible Answers:

Correct answer:

Explanation:

Rewrite the equation in standard form.

In this format, we can identify the coefficients of a, b, and c.

The discriminant is the term inside the square root of the quadratic equation.

Substitute the known values and solve.

The answer is:  

Example Question #1422 : Algebra Ii

Determine the discriminant of the following function:  

Possible Answers:

Correct answer:

Explanation:

The discriminant refers to the term inside the square root of the quadratic function.

The polynomial,  , is given in the standard form:  

Substitute the known coefficients into the discriminant formula.

The answer is:  

Example Question #1423 : Algebra Ii

Determine the discriminant of the following polynomial:  

Possible Answers:

Correct answer:

Explanation:

Reorganize the terms in order of high to lowest power.

This polynomial is then in the form of .

The discriminant is the term inside the square root of the quadratic equation.

Substitute the values into the equation.

The answer is:  

Example Question #1424 : Algebra Ii

Determine the discriminant:  

Possible Answers:

Correct answer:

Explanation:

The discriminant is the term inside the square root of the quadratic equation.

The polynomial is provided in standard form .

Substitute the variables into the equation.

The answer is:  

Example Question #1425 : Algebra Ii

Solve for the discriminant:  

Possible Answers:

Correct answer:

Explanation:

The discriminant is the term inside the square root of the quadratic equation.

Write the formula for the discriminant.

The equation  is already in the form of:

Substitute the known coefficients into the discriminant equation.

The discriminant is:  

Example Question #1426 : Algebra Ii

Determine the discriminant of:  

Possible Answers:

Correct answer:

Explanation:

The equation is given in the form of .

Write the formula for the discriminant.

Identify the coefficients.

Substitute the values into the equation.

The answer is:  

Example Question #121 : Understanding Quadratic Equations

Determine the discriminant of the following polynomial:  

Possible Answers:

Correct answer:

Explanation:

We will need to put this equation in standard parabolic form.

Subtract  on both sides to move it to the right side.

The discriminant is defined as:  

Substitute the coefficients of the equation in the standard form.

The answer is:  

Example Question #281 : Intermediate Single Variable Algebra

Which of the following will best represent a discriminant with complex roots?

Possible Answers:

Correct answer:

Explanation:

According the rule of discriminant, the expression value defines whether if we will have roots for a parabola or complex roots.

The discriminant is:  

If , we do not have real roots.

If , we have real and equal roots.

If , we have real and unequal roots.

Complex roots are not real roots.  This means the discriminant must be negative.

The answer is:  

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