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How to Know If a Quadratic Equation Will Have One, Two or Three Answers

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    • 1). Obtain a quadratic equation for example purposes. For this example, let the equation be 6x^2 - 8x + 2 = 0.

    • 2). Square the value of the b-coefficient. For this example, the b-coefficient is -8, which is 64 when squared.

    • 3). Multiply the a- and c-coefficients together, then multiply their product by 4. In this example, the a-coefficient is 6 and the c-coefficient is 2. Multiplying 6 and 2 together equals 12, which is 48 when multiplied by 4.

    • 4). Subtract the product from Step 3 from the square of the b-coefficient. If the difference between them is equal to zero, then there is one real number as the solution; if the difference is greater than zero, then there are two real solutions; and if the difference is less than zero, then there are two complex solutions. Concluding the example, subtracting 48 from 64 equals 16, which is greater than zero. The example quadratic equation has two real solutions.

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