5.6 quadratic formula & discriminant p. 291 discriminant: b 2 -4ac the discriminant tells you...
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5.6 Quadratic Formula & Discriminant
p. 291
Discriminant: b2-4ac
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
Examples Find the discriminant
and give the number and type of solutions.
a. 9x2+6x+1=0
a=9, b=6, c=1
b2-4ac=(6)2-4(9)(1)
=36-36=0
1 real solution
b. 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
Quadratic Formula(Yes, it’s the one with the song!)
If you take a quadratic equation in standard form (ax2+bx+c=0), and you complete the square, you will get the quadratic formula!
a
acbbx
2
42
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.)
Examples1. 3x2+8x=35
3x2+8x-35=0
a=3, b=8, c= -35
6
420648 x
)3(2
)35)(3(4)8()8( 2 x
6
4848x
6
228x
3
7
6
14
6
228
x
OR
56
30
6
228
x
2. -2x2=-2x+3
-2x2+2x-3=0
a=-2, b=2, c= -3
)2(2
)3)(2(4)2()2( 2
x
4
2442
x
4
202
x
4
5*4*12
x
4
522
i
x
4
52
4
2
i
x
2
5
2
1 ix
Assignment