Quadratic Formula & Discriminant

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Presentation transcript:

Quadratic Formula & Discriminant

Vocabulary Discriminant - tells you how many solutions and what type you will have. If the discriminant is positive – 2 real solutions negative – 2 imaginary solutions zero – 1 real solution

Notice where the discriminant is in the quadratic formula! Formulas Discriminant: b2-4ac Quadratic formula – it is on the EOCT formula sheet Notice where the discriminant is in the quadratic formula!

Examples 9x2+6x-4=0 a=9, b=6, c=-4 b2-4ac=(6)2-4(9)(-4) =36+144=180 2 real solutions c. 9x2+6x+5=0 a=9, b=6, c=5 b2-4ac=(6)2-4(9)(5) =36-180=-144 2 imaginary solutions Find the discriminant and give the number and type of solutions. 9x2+6x+1=0 a=9, b=6, c=1 b2-4ac=(6)2-4(9)(1) =36-36=0 1 real solution

Using the quadratic formula Make equation say = 0 Find the discriminant, take its square root Plug a, b, c, and discriminant into formula simplify

Examples - solve 3x2+8x=35 3x2+8x-35=0 a=3, b=8, c= -35 OR

-2x2=-2x+3 -2x2+2x-3=0 a=-2, b=2, c= -3

3. 4x2+10x=-10x-25 4x2+20x+25=0 a=4, b=20, c=25