Consider the equation (x - a)(x - b) = 0 which has two identical roots. What should be the condition under which (x - a) (x - b) = c has two distinct real roots?
Explanation:
(x - a)(x - b) = 0 having identical roots means a = b Hence, the expression now effectively becomes (x - a)(x - a) = c For x to have different values, we should have c > 0 because at c = 0, we will end up with x = a AND c < 0 is not possible for rational values of a and x. For c > 0, we will have x = a + (c) and x = a - (c)
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