Originally Posted by

**HallsofIvy** Then I suggest you check again.

$\displaystyle \frac{\sqrt{50}}{2}= \frac{5}{2}\sqrt{2}$ is approximately 3.53533, $\displaystyle \sqrt{7/2}$ is approximately 1.87083, and $\displaystyle \sqrt{175}= 5\sqrt{3}$ is approximately 13.22876. $\displaystyle 2x^2- (\frac{\sqrt{50}}{2}+ \sqrt{7/2})x+ \sqrt{175}= 0$ is $\displaystyle 2x^2- 16.76409x+ 13.22876= 0$.

Putting x= 3.53533 into that gives -33.54313 while putting x= 1.87083 into it gives 24.74118. Neither satisifies the equation.

If a and b are roots of a polynomial of the form (x- a)(x- b)= 0 then we have $\displaystyle x^2- (a+ b)x+ ab= 0$

Now, with $\displaystyle a= \frac{\sqrt{50}}{2}$ and $\displaystyle b= \sqrt{7/2}$, that would be $\displaystyle x^2- (\frac{\sqrt{50}}+ \sqrt{7/2})x+ \sqrt{175}= 0$. But that is NOT what you have- you have an extra "2" multiplying $\displaystyle x^2$.