SOLUTION: Hello all! Thank God for the Matha Tutors!. Could someone please help me get with this one? Here it is: z^2 + 11/2z = -6, The answer in the book say its (-3/4,-4) Could some

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Question 17983: Hello all!
Thank God for the Matha Tutors!. Could someone please help me get with this one? Here it is:
z^2 + 11/2z = -6, The answer in the book say its (-3/4,-4)
Could someone explain this to me?
Thanks to all,
AC

Answer by xcentaur(357)   (Show Source): You can put this solution on YOUR website!
z^2 + 11/2z = -6
z^2 + 11/2z + 6 = 0
Now this is a quadratic equation which can be solved as:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=6.25 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -1.5, -4. Here's your graph:


Now the solution we get,as you see above,is different from what your book says.
Lets check according to the book.


Now the book says the roots are (-3/4 and -4).
then the expression would become





This is the equation you would need to obtain the roots given in your book.


Hope this helps,
Prabhat

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