How do you calculate the discriminant for the equation $$3x^2 - 19x = -20$$ ?

First, rewrite the equation in standard form: $$3x^2 - 19x + 20 = 0$$ . Then, the discriminant is $$D = (-19)^2 - 4(3)(20) = 361 - 240 = 121$$ .

Solve the equation $$2x^2 + 2x - 12 = 0$$ using the quadratic formula.

Using the quadratic formula, we find $$x = \frac{{-2 \pm \sqrt{{2^2 - 4(2)(-12)}}}}{{2(2)}} = \frac{{-2 \pm \sqrt{{4 + 96}}}}{{4}} = \frac{{-2 \pm 10}}{{4}}$$ . Thus, $$x = 2$$ or $$x = -3$$ .

What is the first step in using the quadratic formula?

The first step is to identify the coefficients a, b, and c from the standard form of the quadratic equation $$ax^2 + bx + c = 0$$ .

What error did the student make when substituting values into the quadratic formula?

The student used $$b$$ instead of $$-b$$ as the first term in the numerator when substituting values into the formula.

If the discriminant is 76, what can we conclude about the solutions?

Since the discriminant is positive (76), we conclude that there are two distinct real solutions.

What is the correct setup of the discriminant for the equation $$3x^2 - 19x = -20$$ ?

The correct setup is $$(-19)^2 - 4(3)(20)$$ .

What is the value of the discriminant for the equation $$6x^2 - 2x - 3 = 0$$ ?

The discriminant is calculated as $$D = (-2)^2 - 4(6)(-3) = 4 + 72 = 76$$ .

How do you interpret a discriminant value of 29?

A discriminant value of 29 indicates that the quadratic equation has two distinct real solutions.

What is the general form of a quadratic equation?

The general form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where a, b, and c are constants and $$a \neq 0$$ .

Quadratic Formula and Discriminant Review Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is the Quadratic Formula?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What does the discriminant tell us about a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

What is the significance of a positive discriminant?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

What is the significance of a zero discriminant?

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution, also known as a repeated or double root.

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

What is the significance of a negative discriminant?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, but two complex solutions.

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

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