Question

Which of the following are roots of the polynomial function? check all that apply F(x)=x^3-6x^2+7x-2

Answer 1

Answer:

x = .4384471872, x = 1, x = 4.561552813

Step-by-step explanation:

(x-1) is a root. When you divide it into x³-6x²+7x -2, you are left with x²-5x+2. Use the quadratic equation on that.

(5+/-$\sqrt{25-8}$)/2

So the roots are (5 - $\sqrt{17}$)/2,       1,  and        (5 + $\sqrt{17}$)/2

Answer 2

The roots of the polynomial function are: 4.562, 1, 0.483 and 0.709

Polynomial function

The polynomial function is given as

$F(x) = x^3 - 6x^2 + 7x -2$

Graph

Next, we plot the graph of the function $F(x) = x^3 - 6x^2 + 7x -2$

See attachment

From the attached graph, the function crosses the x-axis at the following points

4.562, 1, 0.483 and 0.709

Hence, the roots of the polynomial function are: 4.562, 1, 0.483 and 0.709

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