SOLUTION: use the quadratic formula to solve the following. leave irrational roots in the simplest radical form . 3m^2+m-2=0 and 5p^2+3p-2=0

Algebra ->  College  -> Linear Algebra -> SOLUTION: use the quadratic formula to solve the following. leave irrational roots in the simplest radical form . 3m^2+m-2=0 and 5p^2+3p-2=0      Log On


   

Question 273328: use the quadratic formula to solve the following. leave irrational roots in the simplest radical form .
3m^2+m-2=0
and
5p^2+3p-2=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
For more help, check out this quadratic formula solver.

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for m:


Starting with the general quadratic


am%5E2%2Bbm%2Bc=0


the general solution using the quadratic equation is:


m+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 3%2Am%5E2%2Bm-2=0 ( notice a=3, b=1, and c=-2)





m+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A3%2A-2+%29%29%2F%282%2A3%29 Plug in a=3, b=1, and c=-2




m+=+%28-1+%2B-+sqrt%28+1-4%2A3%2A-2+%29%29%2F%282%2A3%29 Square 1 to get 1




m+=+%28-1+%2B-+sqrt%28+1%2B24+%29%29%2F%282%2A3%29 Multiply -4%2A-2%2A3 to get 24




m+=+%28-1+%2B-+sqrt%28+25+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




m+=+%28-1+%2B-+5%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




m+=+%28-1+%2B-+5%29%2F6 Multiply 2 and 3 to get 6


So now the expression breaks down into two parts


m+=+%28-1+%2B+5%29%2F6 or m+=+%28-1+-+5%29%2F6


Lets look at the first part:


x=%28-1+%2B+5%29%2F6


m=4%2F6 Add the terms in the numerator

m=2%2F3 Divide


So one answer is

m=2%2F3




Now lets look at the second part:


x=%28-1+-+5%29%2F6


m=-6%2F6 Subtract the terms in the numerator

m=-1 Divide


So another answer is

m=-1


So our solutions are:

m=2%2F3 or m=-1