How do you solve #4x^2+8x+3#?

1 Answer
Aug 19, 2015

Answer:

The solutions are:
# color(blue)(x=-3/2#

#color(blue)(x=-1/2#

Explanation:

#4x^2+8x+3# , solving assuming that the expression is equated to zero.

#4x^2+8x+3=0#

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

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*4 = 12#
and
#N_1 +N_2 = b = 8#

After trying out a few numbers we get #N_1 = 2# and #N_2 =6#
#2*6 = 12#, and #2+6= 8#

#4x^2+8x+3 = 4x^2+2x+6x+3#

# 4x^2+2x+6x+3 = 2x(2x+1) +3(2x+1)#

# (2x+3)(2x+1)=0#

Now we equate factors to zero.
#2x+3=0, color(blue)(x=-3/2#

#x+2=0,color(blue)(x=-1/2#