What I learned in PreCalc 11 this week was what a discriminant is. The discriminant is a part of the quadratic formula (red in picture below) and it tells us if there is 2, 1, or 0 solutions.

The red is the formula used to find the discriminant.

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How we know is that if the final result of  is > 0, then it has 2 solutions. If the answer is = 0, then it has 1 solution and if the answer is < 0 then it has no solution.