Sec. 5-8: Quadratic Formula

Quadratic Formula: Like C.T.S., the quadratic formula can solve ANY quadratic equation. It is simply a matter of substituting a, b, & c into the formula to find the answer(s). *** Remember, you are solving a quadratic equation so you should have 2 solutions, (or multiplicity 2).

The Quadratic Formula Where y = ax2 + bx + c

Solutions will be: x = -2, and 10 Let’s do one example with an equation you already will know the answers to: Solve: x2 – 8x – 20 = 0 Solutions will be: x = -2, and 10 a = 1, b = -8 c = -20

Discriminant The discriminant is just the RADICAND of the quadratic formula: b2 – 4ac The discriminant will tell you how many solutions you will have & what kind. If b2 – 4ac = 0 1 solution—Real If b2 – 4ac > 0 2 solutions – Real If b2 – 4ac < 0 2 solutions – Imaginary Think about the relationship of the √discriminant…these solution types should “make sense”. Follow the next examples.

What kind of solutions did x2 – 8x – 20 =0 have? 2 Real—look at the discriminant… b2 – 4ac = 64 – 4(1)(-20) = 64 + 80 > 0; 2 Real What about 2x2 – 5x + 7 = 0? b2 – 4ac = 25 – 4(2)(7) = 25 – 56 < 0; 2imaginary