Determine the roots of: f(x)=x^{3}-6x^{2}+11x+6

Question:

Determine the roots of: {eq}f(x)=x^{3}-6x^{2}+11x+6 {/eq}

Finding roots of a function:

The roots of a function are those values which when substituted in the variables, satisfy the equation. Basically they are also the zeros of the polynomial.

Answer and Explanation:

We can clearly see that the equation has only one real root as it crosses the {eq}x-axis{/eq} only once and rest it has two complex conjugate roots.

{eq}x^{3}-6x^{2}+11x+6=0{/eq}

Since the function is unsolvable by hit and trial methods,

We find it by a complicated formula or can find it from the graph and finally roots are

{eq}-0.434 , 3.217 + i* 1.856 , 3.217 - i* 1.856{/eq}


Learn more about this topic:

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Factoring Polynomial Expressions

from College Algebra: Help and Review

Chapter 8 / Lesson 4
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