While we can conceivably test the results to be sure Equation 6 leads to the proper root, wouldn't it be nice if our algorithm could assure us one real root in all cases? This is actually an “inverse ...

The second diagram has one root and the third diagram has no roots. The discriminant can be used in the following way: \({b^2} - 4ac\textless0\) - there are no real roots (diagram 1 ...

4ac\). And the types of root the equation has can be worked out as follows: If \({b^2} - 4ac\textgreater0\), the roots are real and unequal (diagram A) If \({b^2} - 4ac = 0\), the roots are real ...