What is the value of the discriminant in the equation $$5x^2 + 3x - 3 = 0$$ ?

The discriminant is calculated as $$b^2 - 4ac = 3^2 - 4(5)(-3) = 9 + 60 = 69$$ .

Solve the equation $$9x^2 - 7x - 4 = 0$$ using the quadratic formula.

Using the quadratic formula, the solutions are $$x = \frac{{7 \text{±} \text{√}(7^2 - 4(9)(-4))}}{{2(9)}} = \frac{{7 \text{±} \text{√}(169)}}{{18}} = \frac{{7 \text{±} 13}}{{18}}$$ .

How do you determine the number of real solutions from the discriminant?

If the discriminant is greater than zero, there are two real solutions; if it is equal to zero, there is one real solution; if it is less than zero, there are no real solutions.

What is the first step in solving a quadratic equation using the quadratic formula?

Identify the coefficients a, b, and c from the standard form of the quadratic equation $$ax^2 + bx + c = 0$$ .

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

The solutions are $$m = \frac{{-2 \text{±} \text{√}(2^2 - 4(2)(-12))}}{{2(2)}} = \frac{{-2 \text{±} \text{√}(100)}}{{4}} = \frac{{-2 \text{±} 10}}{{4}}$$ , giving m = 2 and m = -3.

What does it mean if a quadratic equation has one real solution?

It means the discriminant is zero, indicating that the parabola touches the x-axis at one point (the vertex).

What is the relationship between the coefficients of a quadratic equation and its roots?

The sum of the roots is equal to $$-\frac{b}{a}$$ and the product of the roots is equal to $$\frac{c}{a}$$ .

How can you check if your solutions to a quadratic equation are correct?

Substitute the solutions back into the original equation to see if they satisfy it.

What is the role of the quadratic formula in solving quadratic equations?

The quadratic formula provides a systematic method to find the roots of any quadratic equation, regardless of whether the roots are real or imaginary.

What is the discriminant of the equation $$x^2 + 4x + 4 = 0$$ ?

The discriminant is $$4^2 - 4(1)(4) = 16 - 16 = 0$$ , indicating one real solution.

Explain the term 'real solutions' in the context of quadratic equations.

Real solutions are the x-values where the quadratic function intersects the x-axis, which occur when the discriminant is non-negative.

A2 Quadratic Formula and Discriminant Flashcards

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16 questions

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1.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation indicate?

Back

The discriminant indicates the nature of the roots of a quadratic equation. If it is positive, there are two real solutions; if it is zero, there is one real solution; if it is negative, there are two imaginary solutions.

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

If the discriminant is negative, what can be said about the solutions of the quadratic equation?

Back

There will be two imaginary solutions.

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

If the discriminant is positive, what can be said about the solutions of the quadratic equation?

Back

There will be two real solutions.

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

What is the significance of the term 'imaginary solutions' in quadratic equations?

Back

Imaginary solutions occur when the discriminant is negative, indicating that the quadratic does not intersect the x-axis.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

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