Find the root(s) of f (x) = (x- 6)2(x + 2)2.
options are:
a.-6 with multiplicity 1
b.-6 with multiplicity 2
c.6 with multiplicity 1
d.6 with multiplicity 2
e.-2 with multiplicity 1
f.-2 with multiplicity 2
g.2 with multiplicity 1
h.2 with multiplicity 2

The roots of are and . Option (d) and option (f) are correct.

Further explanation:

The Fundamental Theorem of Algebra states that the polynomial has n roots if the degree of the polynomial is n.

The polynomial function has n roots or zeroes.

Given:

The equation is

Explanation:

The given equation is

According to the Fundamental Theorem of Algebra the function has 4 roots.

Solve the above equation to obtain the zeros.

The roots are

The roots of and .Option (d) and option (f) are correct.

Learn more:

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Polynomial

Keywords: roots, linear equation, quadratic equation, zeros, function, polynomial, solution, cubic function, degree of the function, multiplicity of 1, multiplicity of 2.

b) well because you get well

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3