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How many and of which kind of roots does the equation f(x)=x4−2x3−11x2+12x+36 have?

How many and of which kind of roots does the equation f(x)=x4−2x3−11x2+12x+36 have-example-1

2 Answers

5 votes

The number and kind of roots of the equation f(x) = x⁴ − 2x³ − 11x² + 12x + 36 is

4 real roots

What is root of a polynomial equation

The roots of a polynomial equation are the values of the variable that make the polynomial equal to zero.

In a graph, the root is the point where the graph intersects the x-axis..

Solving the equation graphically shows that the roots has multiplicity at

(-2, 0) and (3, 0)

The roots are

x = -2, -2, 3, 3

These are four real roots

How many and of which kind of roots does the equation f(x)=x4−2x3−11x2+12x+36 have-example-1
User Yevhen Surovskyi
by
4.6k points
3 votes

we have the equation

f(x)=x^4-2x^3-11x^2+12x+36

using a graphing tool

the factors are

(x+2) ----> multiplicity 2

(x-3) -----> multiplicity 2

therefore

The answer is 4 real roots

option C

How many and of which kind of roots does the equation f(x)=x4−2x3−11x2+12x+36 have-example-1
User Nebojsa Susic
by
4.0k points