SOLUTION: If a and b are positive real numbers and each of the equations {{{ x^2+ax+2b=0}}} and {{{x^2+2bx+a=0}}} has real roots, what is the smallest possible value of a+b?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If a and b are positive real numbers and each of the equations {{{ x^2+ax+2b=0}}} and {{{x^2+2bx+a=0}}} has real roots, what is the smallest possible value of a+b?      Log On


   

Question 670823: If a and b are positive real numbers and each of the equations +x%5E2%2Bax%2B2b=0 and x%5E2%2B2bx%2Ba=0 has real roots, what is the smallest possible value of a+b?
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Using the quadratic formula on the first one we get:

Second:

Which when set equal to each other we get b = (a/2) and so b = 2 and a = 4
So a+b = 6