Math Problem Statement

What are the zeros of the polynomial function? y = x(x - 6)(x + 5)

Solution

To find the zeros of the polynomial function y=x(x6)(x+5)y = x(x - 6)(x + 5), we need to set y=0y = 0 and solve for xx.

The equation becomes: x(x6)(x+5)=0x(x - 6)(x + 5) = 0

For the product to be zero, at least one of the factors must be zero. So, we have:

  1. x=0x = 0
  2. x6=0x=6x - 6 = 0 \Rightarrow x = 6
  3. x+5=0x=5x + 5 = 0 \Rightarrow x = -5

Thus, the zeros are 00, 66, and 5-5, making the correct answer "0, 6, -5".

Would you like more details on any of these steps?


  1. What are polynomial roots and why are they important?
  2. How do you factorize a polynomial like this one?
  3. What does the graph of y=x(x6)(x+5)y = x(x - 6)(x + 5) look like?
  4. How can we confirm these solutions by substitution?
  5. How does this function behave as xx approaches infinity?

Tip: To find zeros, always set the equation to zero and solve for each factor individually.

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Math Problem Analysis

Mathematical Concepts

Polynomial Functions
Factoring
Roots of Equations

Formulas

y = x(x - 6)(x + 5) = 0

Theorems

Zero Product Property

Suitable Grade Level

Grades 9-11