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Quadratic equations, which are expressed in the form of ax2 + bx + c = 0

where a does not equal 0, can have more than one solution. Using the
discriminant and graph of a quadratic equation, how can you tell how many real
solutions a quadratic equation will have?

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2 Answers

For an equation in standard form

Ax2 + By + C = 0

The discriminant D is given by

D = B2 - 4AC

For D > 0 ==> two real solutions
      D < 0 ==> two complex solutions (involving imaginary numbers)
      D = 0 ==> one real solution

The best way to find real zeros would be to count how many times the graphed equation crosses the x-axis