# What are the type of roots for the equation?

The equation is $7x²-(7\pi+22)x+22\pi=0$.

I am not sure if i should put the value of $\pi=$ (22/7)or (3.14) or even if I should do that.. The question asks for the type of roots rational or irrational.

• There will be at least one transcendental root. – Zain Patel Jul 17 '16 at 10:30

It seems you've already worked out that $$7x^2-(7\pi+22)x+22\pi = (7x-22)(x-\pi)$$ so the solutions to the equation are $\frac{22}{7}$ and $\pi$.
Importantly, note that $\pi \ne 3.14$. Rounding solutions to a finite number of decimal places will magically turn any irrational solutions into rational ones, which probably isn't a good thing if you're asked to find out whether solutions are rational or irrational.
So the question asks if the solutions for the equation are rational or irrational. If you solve the equation you get solutions (=roots) $\pi$ (irrational) and $\frac{22}{7}$ (rational).