Algebra
posted by Vilma on .
I need help doing this problem, should I not get the same answer with each technique? Please help.
What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation:
2x² + 3x + 1 = 0

1. Factoring (works only in special cases)
(2x+1)(x+1) = 0
2x+1=0 or x+1=0
x = 1/2 or x = 1
2. completing the square, works all the time
(I use this method when the coefficient of the square term is 1 and the middle term is even)
divide by 2
x^2 + (3/2)x = 1/2
take 1/2 the coefficient of the middle term, square it and add it to both sides
x^2 + (3/2)x + 9/16 = 1/2 + 9/16
(x+ 3/4)^2 = 1/16
take √ of both sides
x+3/4 = ± 1/4
x = 3/4 ± 1/4
x = 1/2 or x = 1
3. The quadratic formula, works all the time.
x = (3 ± √(94(2)(1))/4
= (3 ±√1)/4
= 1/2 or 1