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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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) About Me  (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:

%28x-7%29%5E2%28x%5E2%2B7%29=0


%28x-7%29%5E2=0 or x%5E2%2B7=0 Use the zero product property to break up the factors


Let's solve the first equation: %28x-7%29%5E2=0


%28x-7%29%5E2=0 Start with the given equation


x-7=0 Take the square root of both sides to eliminate the square on the left side.


x=7 Add 7 to both sides.


So the first solution is x=7


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Now let's solve the second equation: x%5E2%2B7=0


x%5E2%2B7=0 Start with the given equation


x%5E2=-7 Subtract 7 from both sides.


x=sqrt%28-7%29 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 x=i%2Asqrt%287%29 or x=-i%2Asqrt%287%29


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Answer:


So the solution(s) are

x=7, x=i%2Asqrt%287%29 or x=-i%2Asqrt%287%29


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