Quadratic Functions

Question

Solve the equation f(x) = 0 for each of the following quadratic functions:

f (x)=2x2 +4x+3

PLEASE HELP ME OUT?!

Answer 1

2x^2 + 4x + 3 = 0

general form of the equation is

ax^2 + bx + c = 0. You can try factoring, complete the square or use the quadratic formula where

x = -b/2a + or - (1/2a)sqr(b^2 -4ac)

it doesn't seem to easily factor, as there are no real solutions. the discriminate is negative, so there are just imaginary solutions.

divide by 2 to get x^2 +2x + 3/2 =0

complete the square by taking half of the x coefficient and square it. 2/2 = 1

add it to both sides

x^2 +2x + 1 = 1-3/2 = -1/2

(x+1)^2 = -1/2

x+1 = + or - sqr(-1/2)

x = -1 + or - isqr(1/2)

x=-1 + or - i/sqr2

or use the quadratic formula

x = -4/4 + or - (1/4)sqr(16-4(2)(3))

= -1 + or - (1/4)sqr(-8)

= -1 + or - i/sqr2