Answer :
To find the zeros of the given polynomials, we'll go through each equation step-by-step.
### Equation 1: [tex]\(x^3 + x^2 - 8x = 12\)[/tex]
1. Rearrange the Equation:
We need to bring all the terms to one side of the equation to set it equal to zero.
[tex]\[
x^3 + x^2 - 8x - 12 = 0
\][/tex]
2. Find the Zeros:
We solve for the values of [tex]\(x\)[/tex] that make this equation true. These values are called the zeros of the polynomial.
- The solutions to the equation are [tex]\(x = -2\)[/tex] and [tex]\(x = 3\)[/tex].
### Equation 2: [tex]\(x^3 - 5x^2 + 48 = 8x\)[/tex]
1. Rearrange the Equation:
Again, we bring all terms to one side to have the equation equal to zero.
[tex]\[
x^3 - 5x^2 - 8x + 48 = 0
\][/tex]
2. Find the Zeros:
We solve for the values of [tex]\(x\)[/tex] that satisfy the equation.
- The solutions to this equation are [tex]\(x = -3\)[/tex] and [tex]\(x = 4\)[/tex].
So, the zeros for the first equation are [tex]\([-2, 3]\)[/tex], and for the second equation, they are [tex]\([-3, 4]\)[/tex].
### Equation 1: [tex]\(x^3 + x^2 - 8x = 12\)[/tex]
1. Rearrange the Equation:
We need to bring all the terms to one side of the equation to set it equal to zero.
[tex]\[
x^3 + x^2 - 8x - 12 = 0
\][/tex]
2. Find the Zeros:
We solve for the values of [tex]\(x\)[/tex] that make this equation true. These values are called the zeros of the polynomial.
- The solutions to the equation are [tex]\(x = -2\)[/tex] and [tex]\(x = 3\)[/tex].
### Equation 2: [tex]\(x^3 - 5x^2 + 48 = 8x\)[/tex]
1. Rearrange the Equation:
Again, we bring all terms to one side to have the equation equal to zero.
[tex]\[
x^3 - 5x^2 - 8x + 48 = 0
\][/tex]
2. Find the Zeros:
We solve for the values of [tex]\(x\)[/tex] that satisfy the equation.
- The solutions to this equation are [tex]\(x = -3\)[/tex] and [tex]\(x = 4\)[/tex].
So, the zeros for the first equation are [tex]\([-2, 3]\)[/tex], and for the second equation, they are [tex]\([-3, 4]\)[/tex].
