Question

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

Answer 1

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`