How to apply the quadratic formula to a quadratic with fractions

The video tutorial explains how to handle quadratic equations, focusing on graph transformations and eliminating fractions. It covers the use of the discriminant to determine solution types and demonstrates finding complex roots using the quadratic formula. The tutorial emphasizes simplifying equations by removing fractions and understanding the implications of the discriminant in identifying real and complex solutions.

What happens to the solutions of a quadratic equation when each term is multiplied by a constant?

• The solutions become imaginary.

• The solutions change.

• The solutions become complex.

• The solutions remain the same.

What is the least common denominator used to eliminate fractions in the given quadratic equation?

• 3

• 2

• 6

• 4

What is the value of the discriminant in the quadratic equation discussed?

• 729

• -135

• 864

• 135

What type of solutions does a negative discriminant indicate?

• Two real solutions

• One real solution

• No real solutions

• Two complex solutions

How is the square root of a negative number represented in the complex number system?

• As a real number

• As an imaginary number

• As a rational number

• As a whole number

What is the simplified form of the complex roots found in the quadratic equation?

• X = 9 ± sqrt 15 / 4

• X = 27 ± sqrt 15 / 12

• X = 27 ± sqrt 15 I / 12

• X = 9 ± sqrt 15 I / 4

Which number is used to simplify the expression of the complex roots?

• 5

• 4

• 3

• 2