Solve the quadratic equation: $$36x^2 + 169 = 0$$

$$x = \text{±}\frac{13}{6}i$$ .

Solve the equation: $$-1 + 5p^2 = -86$$

$$p = \text{±}i\text{sqrt}{17}$$ .

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where a, b, and c are constants and @@a eq 0@@.

How do you determine if a quadratic has real or imaginary solutions?

Calculate the discriminant $$b^2 - 4ac$$ . If it is negative, the solutions are imaginary.

What is the vertex form of a quadratic equation?

The vertex form is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line that divides the parabola into two mirror images, given by the formula $$x = -\frac{b}{2a}$$ .

What is the significance of the 'i' in imaginary numbers?

The 'i' represents the imaginary unit, defined as $$i = \text{sqrt}(-1)$$ , allowing for the solution of equations that do not have real solutions.

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

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

Solving Quadratics with Imaginary Numbers Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the square root method for solving quadratics?

Back

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What does it mean to have imaginary solutions in a quadratic equation?

Back

Tags

CCSS.HSN.CN.A.1

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.A.2

7.

FLASHCARD QUESTION

Front

What is the discriminant in a quadratic equation?

Back

Tags

CCSS.HSA-REI.B.4B

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