I need help with number 3. I forgot how to even start the problem off to find th

Question

I need help with number 3. I forgot how to even start the problem off to find the roots and the multiplicity of each root.

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Ready to Go On? Finding Real Roots of Polynomial Equations 1. The Yearly profit of a company in thousands of dollars can be modeled by P(t) = t^4 - 10t^2 + 9, where t is the number of years since 2000. Factor to find years in which the profit was 0. 2. A rectangular prism has a length that is twice its width and a height that is twice its width and a height that is 4 longer than its width. The volume of the rectangular prism is 48 cubic meter. What is the width of the rectangular prism? Identify the roots of each equation. State the multiplicity of each toot 3. x^3 + 6x^2 + 12x + 8 = 0 4. 2x^3 + 8x^2 - 32x - 128 = 4,096 0 5. x^4 - 6 Fundamental Theorem of Algebra Write the simplest polynomial function with the given mots. the equation by finding all roots

Explanation / Answer

Hi..

Given equation : x^3 + 6x^2 + 12x + 8 = 0

Write the left hand side as a cube: (x+2)^3 = 0

Take the cube roots of both sides: x+2 = 0

Subtract 2 from both sides: x = - 2

and the multiplicity of x = -2 is the power of (x + 2), then multiplicity of -2 is 3.

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