How do you solve #2x^2 - 7x + 6 = 0# by factoring?

1 Answer
Aug 16, 2015

Answer:

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

# color(blue)(x=2#

Explanation:

#2x^2−7x+6=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 = 2*6 = 12#
AND
#N_1 +N_2 = b = -7#

After trying out a few numbers we get #N_1 = -3# and #N_2 =-4#
#-3*-4 = 12#, and #-3+(-4)= -7#

#2x^2−7x+6=0 =2x^2−4x-3x+6 #

#2x(x-2) -3(x-2)=0#

#(2x-3)(x-2) =0#

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

#x-2 =0, color(blue)(x=2#