![]() Ī third method of solving quadratic equations that works with both real and imaginary roots is called completing the square. Since the discriminant b 2 – 4 ac is negative, this equation has no solution in the real number system.īut if you were to express the solution using imaginary numbers, the solutions would be. The quadratic formula can also be used to solve quadratic equations whose roots are imaginary numbers, that is, they have no solution in the real number system. Since the discriminant b 2 – 4 ac is 0, the equation has one root. Then substitute 1, 2, and –2 for a, b, and c, respectively, in the quadratic formula and simplify. In Example, the quadratic formula is used to solve an equation whose roots are not rational. Then substitute 1 (which is understood to be in front of the x 2), –5, and 6 for a, b, and c, respectively, in the quadratic formula and simplify.īecause the discriminant b 2 – 4 ac is positive, you get two different real roots.Įxample produces rational roots.
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