How do you factor and solve #3x^2+5x+2=0#?

1 Answer
May 24, 2016

Answer:

The solutions for the equation are

#color(green)(x = -2/3#

#color(green)(x = -1#

Explanation:

#3x^2 + 5x + 2 = 0 #

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 3*2 = 6#

AND

#N_1 +N_2 = b = 5#

After trying out a few numbers we get #N_1 = 3# and #N_2 =2#
#3*2 = 6#, and #3 + 2= 5#

Factorising the expression:

#3x^2 +color(blue)( 5x) + 2 = 3x^2 + color(blue)(3x + 2x) + 2 #

# = 3x(x + 1 ) + 2 ( x + 1 )#

#(x +1 )# is a common factor to each of the terms

#=color(blue)((3x + 2 ) ( x + 1 )#

We now equate the factors to zero to obtain the solutions:

  • #3x + 2 = 0, color(green)(x = -2/3#

  • #x +1 = 0, color(green)(x = -1#