How do you solve #x^2 + 5x - 6 = 0# by factoring?

Question

3582 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-29T13:02:03

The solutions are

#color(blue)(x=1 #

#color(blue)(x=-6 #

#x^2+5x−6=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 = 1*-6 = -6#

AND

#N_1 +N_2 = b = 5#

After trying out a few numbers we get #N_1 = 6# and #N_2 =-1#

#6*-1 = -6#, and #6+(-1)= 5#

#x^2+5x−6=x^2+6x-1x−6#

#=x(x+6) - 1(x+6)#

#=(x-1)(x+6) #

Now we equate the factors to zero:

#x-1=0 , color(blue)(x=1 #

#x+6=0 , color(blue)(x=-6 #

Answer 2 · 2015-09-29T17:06:57

Solve y = x^2 + 5x - 6 = 0

Ans: 1 and (-6)

Since (a + b + c = 0), use the Shortcut. The 2 real roots are: 1 and (c/a) = -6.