SOLUTION: Please help! I have tried every way possible and cannot figure these out! #70) b^4+13b^2+36=0 #30) -3x^2-2x-5=0 #42) 9m^2+16=24mn Thank you in advance for your he

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help! I have tried every way possible and cannot figure these out! #70) b^4+13b^2+36=0 #30) -3x^2-2x-5=0 #42) 9m^2+16=24mn Thank you in advance for your he      Log On


   

Question 201277: Please help! I have tried every way possible and cannot figure these out!
#70) b^4+13b^2+36=0

#30) -3x^2-2x-5=0

#42) 9m^2+16=24mn

Thank you in advance for your help!


Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
b%5E4%2B13b%5E2%2B36=0
%28b%5E2%2B9%29%28b%5E2%2B4%29=0
%28b%2B3i%29%28b-3i%29%28b%2B2i%29%28b-2i%29=0
b = 3i, -3i, 2i, -2i
http://www77.wolframalpha.com/input/?i=+b^4%2B13b^2%2B36%3D0
-3x%5E2-2x-5=0
Use this URL --> http://www.algebra.com/algebra/homework/quadratic/quadratic.solver
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -3x%5E2%2B-2x%2B-5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A-3%2A-5=-56.

The discriminant -56 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -56 is + or - sqrt%28+56%29+=+7.48331477354788.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-3%2Ax%5E2%2B-2%2Ax%2B-5+%29

%28-3x%2B5%29%28x-1%29=0
x=5/3 and 1

9m%5E2%2B16=24mn
9m%5E2-24mn%2B16=0
I am guessing you left off an n^2
9m%5E2-24mn%2B16n%5E2=0
%283m-4%29%283m-4%29=0
m=4/3
http://www77.wolframalpha.com/input/?i=9x^2-24xy%2B16y^2%3D0