(y-7)^2(y+9)=0

Jasonbradley

2 min read

·

Jun 17, 2024

14

Share

Solving the Equation (y-7)^2(y+9) = 0

This equation is a polynomial equation with a degree of 3 (because the highest power of y is 3). We can solve it by using the Zero Product Property.

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

In this case, we have three factors:

• (y-7)^2
• (y+9)

For the entire expression to equal zero, at least one of these factors must equal zero.

Solving for the Factors

Let's solve for each factor individually:

• (y-7)^2 = 0

  • Taking the square root of both sides: y - 7 = 0
  • Adding 7 to both sides: y = 7
  • Since (y-7) is squared, this solution has a multiplicity of 2.

• (y+9) = 0

  • Subtracting 9 from both sides: y = -9

The Solutions

Therefore, the solutions to the equation (y-7)^2(y+9) = 0 are:

• y = 7 (multiplicity of 2)
• y = -9

This means that the equation has two distinct roots, with one of them (y = 7) having a multiplicity of 2. This means the graph of the function touches the x-axis at y = 7 without crossing it.