Does the discriminant with a value of 49 indicate that the quadratic equation has (a) 2 real solutions or (b) 2 rational solutions, and why? Also, what's the difference?
cheers
is 49 then you have two solutions because the solutions of $\displaystyle x=\frac{-b\pm7}{2a}$ using the quadratic formula and as you can see you have two solutions $\displaystyle \frac{-b+7}{2a}$ and $\displaystyle \frac{-b-7}{2a}$...to have only one solution you need your discriminant to be zero so the value of x that makes the polynomial zero is given by $\displaystyle x=\frac{-b\pm0}{2a}$ which just gives $\displaystyle \frac{-b}{2a}$ as your answer...and finally to have zero solutions you need the discriminant to be negative because your answer will be$\displaystyle \frac{-b\pm{ic}}{2a}$ where$\displaystyle i=(-1)^{\frac{1}{2}}$...and since $\displaystyle i$ is an imaginary number there are no REAL solutions