Understanding Zeros of a Cubic Function

The video tutorial explains how to find the zeros of a cubic function by setting the function equal to zero and solving the resulting equation. It demonstrates factoring by grouping to simplify the equation and find the zeros, which include one real zero and two complex zeros. The tutorial also includes graphing the function to verify the real zero, while explaining why complex zeros are not visible on the graph.

What is the first step in finding the zeros of a cubic function?

• Set the function equal to zero

• Differentiate the function

• Integrate the function

• Graph the function

What technique is used to factor the given cubic equation?

• Factoring by grouping

• Factoring by substitution

• Factoring by division

• Factoring by expansion

What is the greatest common factor of the terms x^3 + 5x^2?

• 5

• 5x

• x

• x^2

Tags

CCSS.HSF-IF.C.7C

After factoring, what equation do we solve to find the real zero?

• x^3 + 5x^2 = 0

• x^2 + 3 = 0

• x + 5 = 0

• 3x + 15 = 0

What is the real zero of the cubic function?

• -3

• 3

• -5

• 5

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

What is the result of solving x^2 + 3 = 0?

• x = ±i√3

• x = ±√3

• x = ±√-3

• x = ±3i

Tags

CCSS.HSN.CN.A.1

What is the imaginary unit 'i' equivalent to?

• √-1

• 1

• √1

• -1

How many complex zeros does the cubic function have?

• None

• Three

• Two

• One

Why are complex zeros not visible on the graph?

• They are not plotted

• They are too small

• They are not real numbers

• They are too large

What is the x-intercept of the cubic function on the graph?

• (-5, 0)

• (5, 0)

• (0, 5)

• (0, -5)