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5.6 Quadratic Formula & Discriminant p. 291

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Discriminant: b 2 -4ac The discriminant tells you how many solutions and what type you will have. If the discrim: Is positive – 2 real solutions Is negative – 2 imaginary solutions Is zero – 1 real solution

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Examples Find the discriminant and give the number and type of solutions. a. 9x 2 +6x+1=0 a=9, b=6, c=1 b 2 -4ac=(6) 2 -4(9)(1) =36-36=0 1 real solution b. 9x 2 +6x-4=0 a=9, b=6, c=-4 b 2 -4ac=(6) 2 -4(9)(-4) =36+144=180 2 real solutions c. 9x 2 +6x+5=0 a=9, b=6, c=5 b 2 -4ac=(6) 2 -4(9)(5) =36-180=-144 2 imaginary solutions

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Quadratic Formula (Yes, it’s the one with the song!) If you take a quadratic equation in standard form (ax 2 +bx+c=0), and you complete the square, you will get the quadratic formula!

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When to use the Quadratic Formula Use the quadratic formula when you can’t factor to solve a quadratic equation. (or when you’re stuck on how to factor the equation.)

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Examples 1. 3x 2 +8x=35 3x 2 +8x-35=0 a=3, b=8, c= -35 OR

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2. -2x 2 =-2x+3 -2x 2 +2x-3=0 a=-2, b=2, c= -3

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