SOLUTION: solve for the zeros or roots of this polynomial equation r(x)= (x-7)^2 times (x^2+7) Please Please explain step by step because I really want to learn how to solve for the ze

Question 164565: solve for the zeros or roots of this polynomial equation
r(x)= (x-7)^2 times (x^2+7)
Please Please explain step by step because I really want to learn how to solve for the zeros of polynomial equations. Thank you for any help. Please Help Soon!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"Zeros" or "roots" are simply math speak for values of x that make the ENTIRE equation equal to zero (note: "zeros" are not necessarily equal to zero)

So this means that we set the right side equal to zero like this:

or Use the zero product property to break up the factors

Let's solve the first equation:

Start with the given equation

Take the square root of both sides to eliminate the square on the left side.

Add 7 to both sides.

So the first solution is

----------------------------------

Now let's solve the second equation:

Start with the given equation

Subtract 7 from both sides.

Take the square root of both sides.

Since you CANNOT take the square root of a negative number, this means:

a) there are NO real solutions (for this part), and
b) there are two complex (ie imaginary) solutions (if you have never heard of complex/imaginary solutions, then just ignore this next part)

So the two complex imaginary solutions are or

===========================================

Answer:

So the solution(s) are

, or

Ignore the last two solutions if you have never heard of complex/imaginary solutions before.

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