Answer:
x=-2 us the root of polynomial
Step-by-step explanation:
We have been given a polynomial [tex]x^3-4x^2+x+26[/tex]
Root of a polynomial is that point where polynomial vanishes or gives the value zero at that point
We will assume a point by our choice which we can say a hit and trial method which will give the value zero
So, let us assume x=-2 is the root we will put x=-2 in the given polynomial we get
[tex](-2)^3-4(-2)^2+(-2)+26[/tex]
[tex]\Rightarrow -8-16-2+26=0[/tex]
Hence, this is the point where polynomial gives the zero.
Hence, x=-2 is root of polynomial or (x+2)is root of polynomial.
Answer:
The root of the polynomial is equal to [tex]x=-2[/tex]
Step-by-step explanation:
we have
[tex]x^{3}-4x^{2} +x+26=0[/tex]
we know that
The roots of the polynomial are the values of x when the value of the polynomial is equal to zero ( x-intercepts)
Using a graphing tool
see the attached figure
The polynomial has only one x-intercept
For [tex]x=-2[/tex] -----> the value of the polynomial is equal to zero
therefore
The root of the polynomial is equal to [tex]x=-2[/tex]
