Algebra/Quadratic Equation

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The solutions to the general-form quadratic function can be given by a simple equation called the quadratic equation. To solve this equation, recall the completed square form of the quadratic equation derived in the previous section:

In this case, since we're looking for the root of this function. To solve, first subtract c and divide by a:

Take the (plus and minus) square root of both sides to obtain:

Subtracting from both sides:

This is the solution but it's in an inconvenient form. Let's rationalize the denominator of the square root:

Now, adding the fractions, the final version of the quadratic formula is:

This formula is very useful, and it is suggested that the students memorize it as soon as they can.


The part under the radical sign, , is called the discriminant, . The value of the discriminant tells us some useful information about the roots.

  • If , there are two unique real solutions.
  • If , there is one unique real solution.
  • If , there are two unique, conjugate imaginary solutions.
  • If is a perfect square then the two solutions are rational, otherwise they are irrational conjugates.

Word Problems[edit]

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