QuadraticEquations

Quadratic Equations

Equations of the form ax²+bx+c = 0

May have two, one, or no roots (solutions)

May be solved by:

Solution by factoring

factoring: (x-2)(x-3)=0

thus: (x-2)=0 Ţ x=2

Solve for x:

3x²+5x=0

2x²-7x+6=0

15x²-6=x

Solution by formula

If ax²+bx+c = 0

Then x = (-b ą Ö (b²-4ac))/(2a)

Example

Given: x²-5x+6=0

Then: a=1, b=-5, c=6

Therefore: x=(-(-5) ą Ö(-5²-4´1´6))/(2´1)

Thus: x=(5 ą Ö(25-24))/2

And: x=(5 ą 1)/2 Ţ x=3 and x=2

Solve for x:

3x²+6x-11=0

2x²-3x=5

7x²+16=0