The quadratic formula states that ________. x = -b ± √(b² - 4ac)/2a. The part we're interested in is b² - 4ac, this is called the discriminant. I know from school that we can use the discriminant to figure out how many zeroes a quadratic equation has (or rather, if it has complex, real, or repeating zeroes). If b² - 4ac > 0, then the equation has 2 real zeroes. If b² - 4ac < 0, then the equation has 2 complex zeroes. If b² - 4ac = 0, then the equation has repeating zeroes. But I don't understand why this works. Can you explain why the discriminant helps determine the number of zeroes in a quadratic equation?