What are the type of roots for the equation?

Question

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.

Answer 1

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 $\pi$.

By the sounds of it, you now just need to indicate whether each of these solutions is rational or irrational.

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.

Answer 2

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).