![]() When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive but not a perfect square then the roots of the quadratic equation ax 2 + bx + c = 0 are real, irrational and unequal. Case V: b 2 – 4ac > 0 and not perfect square.When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive and perfect square, then the roots α and β of the quadratic equation ax 2 + bx + c = 0 are real, rational and unequal. Case III: b 2– 4ac 0 and perfect square. ![]() When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax 2+ bx + c = 0 are real and equal. When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive, then the roots α and β of the quadratic equation ax 2 +bx+ c = 0 are real and unequal. Let us recall the general solution, α = (-b-√b 2-4ac)/2a and β = (-b+√b 2-4ac)/2a
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