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

A quadratic equation can have three different types of solutions for its roots or answers. The first type of solution is a single real root, the second type has two different real roots, and the third type is a solution with no real roots but two complex or abstract roots. The key to finding the type of solution is the discriminant, b^2 - 4ac, which takes its values from the coefficients in a quadratic equation with the form ax^2 + bx + c. By employing its discriminant, you can find one of the three types of solutions for a quadratic equation without actually having to solve for its answers.

Instructions

- 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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