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quadratic equations have 2 solutions; except when the discriminate = 0. Then there is a duplicate of one solution, or a "double root", or multiplicity of 2.

ex. 2x^2 -8x + 8 = 0 b^2 - 4ac = 64 - (4*2*8) = 0; where a double root occurs.

sometimes you can factor the quadratic equation into two terms. If you can do that quickly and easily, it's faster than using the quadratic equation. For example, say you factor a q.e. into:

(x+5)(x-3). The two answers or roots are x = -5 and x =3. Either of which would make the result 0.

Examples:

**x2 - 3x + 1 = 0**

**2w2 - 4w - 5 = 0**

**z2 - z - 3 = 0**

**5x2 + x - 1 = 0**