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

Question

27419 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-16T17:10:45

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

$color(blue)(x=2$

$2x^2−7x+6=0$

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.
$2x-3 =0, color(blue)(x=3/2$

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

How do you solve 2x^2 - 7x + 6 = 02x^2 - 7x + 6 = 0 by factoring?