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Algebra II : Discriminants

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Example Questions

Example Question #281 : Intermediate Single Variable Algebra

Determine the discriminant of the following function: y=3x^2-5x

Possible Answers:

Correct answer:

Explanation:

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

D= b^2-4ac

The polynomial, y=3x^2-5x , is given in the standard form:

y=ax^2+bx+c

Substitute the known coefficients into the discriminant formula.

(-5)^2-4(3)(0) = 25

The answer is:

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Example Question #282 : Intermediate Single Variable Algebra

Determine the discriminant of the following polynomial: y=-9x+9x^2+5

Possible Answers:

261

Correct answer:

Explanation:

Reorganize the terms in order of high to lowest power.

This polynomial is then in the form of y=ax^2+bx+c .

$y=-9x+9x^2+5 \rightarrow y=9x^2-9x+5$

a=9, b=-9, c=5

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

D= b^2-4ac

Substitute the values into the equation.

D=(-9)^2-4(9)(5) = 81-180 =-99

The answer is:

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Example Question #283 : Intermediate Single Variable Algebra

Determine the discriminant: y=4x^2-3x

Possible Answers:

$\textup{Cannot be determined.}$

Correct answer:

Explanation:

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

D=b^2-4ac

The polynomial is provided in standard form y=ax^2+bx+c .

a=4, b=-3, c=0

Substitute the variables into the equation.

D=b^2-4ac = (-3)^2-4(4)(0) = 9

The answer is:

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Example Question #284 : Intermediate Single Variable Algebra

Solve for the discriminant: y=8x^2-9x+10

Possible Answers:

401

329

241

Correct answer:

Explanation:

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

Write the formula for the discriminant.

D=b^2-4ac

The equation y=8x^2-9x+10 is already in the form of:

y=ax^2+bx+c

Substitute the known coefficients into the discriminant equation.

D=b^2-4ac = (-9)^2 - 4(8)(10) = 81-320= -239

The discriminant is:

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Example Question #285 : Intermediate Single Variable Algebra

Determine the discriminant of: y=-100x^2-50

Possible Answers:

2500

20000

2900

2100

Correct answer:

Explanation:

The equation is given in the form of y=ax^2+bx+c .

Write the formula for the discriminant.

D=b^2-4ac

Identify the coefficients.

a=-100, b=0, c=-50

Substitute the values into the equation.

D= 0-4(-100)(-50) = -20000

The answer is:

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Example Question #286 : Intermediate Single Variable Algebra

Determine the discriminant of the following polynomial: x^2+y=4

Possible Answers:

Correct answer:

Explanation:

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

y=ax^2+bx+c

Subtract x^2 on both sides to move it to the right side.

x^2+y-x^2=4-x^2

y=-x^2+4

The discriminant is defined as: D=b^2-4ac

Substitute the coefficients of the equation in the standard form.

a=-1, b=0, c=4

D=b^2-4ac=0-4(-1)(4) =16

The answer is:

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Example Question #287 : Intermediate Single Variable Algebra

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

Possible Answers:

2000

$\frac{7}{6}$

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: D=b^2-4ac

If D<0 , we do not have real roots.

If D=0 , we have real and equal roots.

If D>0 , 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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Example Question #291 : Intermediate Single Variable Algebra

Evaluate the discriminant, if any: x^2-2y-6 = 2x

Possible Answers:

$\textup{The discriminant cannot be determined.}$

$\frac{5}{3}$

Correct answer:

Explanation:

The formula to determine the discriminant is: D=b^2-4ac

To determine the discriminant, we will need to put the equation in standard form:

y=ax^2+bx+c

Add on both sides.

x^2-2y-6 +2y= 2x+2y

x^2-6= 2x+2y

Subtract on both sides.

x^2-6-2x= 2x+2y-2x

Reorder the terms on the left.

x^2-2x-6 = 2y

Divide by two on both sides.

$\frac{x^2-2x-6 }{2}= \frac{2y}{2}$

The equation in standard form is: $y=\frac{1}{2}x^2-x-3$

The coefficients can be determined to calculate the discriminant.

$a=\frac{1}{2}, b=-1, c=-3$

Substitute the values into the formula.

$D=2b^2-4ac = (-1)^2-4(\frac{1}{2})(-3) = 1+6 = 7$

The answer is:

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Example Question #292 : Intermediate Single Variable Algebra

Determine the discriminant: y=-3x^2-5x

Possible Answers:

Correct answer:

Explanation:

The formula for the discriminant is:

D=b^2-4ac

Given the polynomial in standard format, we can identify the coefficients of the polynomial to substitute into the equation.

a=-3, b=-5, c=0

Substitute all the numbers into the equation.

D=b^2-4ac = (-5)^2-4(-3)(0) = 25

The answer is:

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Example Question #293 : Intermediate Single Variable Algebra

Evaluate the discriminant: y=8x^2-4

Possible Answers:

128

256

Correct answer:

128

Explanation:

Write the formula for the discriminant. The discriminant is the term inside the square root of the quadratic formula.

D=b^2-4ac

Determine the coefficients.

a=8, b=0, c=-4

Substitute the terms into the formula.

D=0^2-4(8)(-4) = 128

The answer is: 128

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Algebra II : Discriminants

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #281 : Intermediate Single Variable Algebra

Example Question #282 : Intermediate Single Variable Algebra

Example Question #283 : Intermediate Single Variable Algebra

Example Question #284 : Intermediate Single Variable Algebra

Example Question #285 : Intermediate Single Variable Algebra

Example Question #286 : Intermediate Single Variable Algebra

Example Question #287 : Intermediate Single Variable Algebra

Example Question #291 : Intermediate Single Variable Algebra

Example Question #292 : Intermediate Single Variable Algebra

Example Question #293 : Intermediate Single Variable Algebra

All Algebra II Resources

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