help please !!!!

Find the rational zero of the polynomial fucntion and use it to find all the zeros of the fucntion.

Question

help please !!!!

Find the rational zero of the polynomial fucntion and use it to find all the zeros of the fucntion.

marcelie · Answer

attachment

marcelie · Answer

what am i doing wrong ?

marcelie · Answer

@mathmale

directrix · Answer

@marcelie   Your work is correct. Why do you think something is wrong with it?

directrix · Answer

x^3 -8x^2+ 19x -14 = 0  is the equation, right?

marcelie · Answer

because my answer sheet says {2, 3 + 2, 3 - 2}

marcelie · Answer

shouldnt there be two 2's

directrix · Answer

The degree of 3 of x^3 -8x^2+ 19x -14 = 0  tells us that there will be 3 zeros.

You correctly found the rational zero of x = 2.

Then, you correctly found the other two roots:  3 -√2  and 3 + √2.

That is a total of 3 zeros.

directrix · Answer

>shouldnt there be two 2's

No.  Two will be a double root, if the graph of the polynomial is tangent to the x-axis.

Look at the attached graph of   x^3 -8x^2+ 19x -14 = P(x).

The graph is not tangent to the x-axis.