How do you factor and solve $3x^2+5x+2=0$ ?

Question

1404 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-24T15:29:42

The solutions for the equation are

$color(green)(x = -2/3$

$color(green)(x = -1$

$3x^2 + 5x + 2 = 0$

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:

$N_1*N_2 = a*c = 3*2 = 6$

AND

$N_1 +N_2 = b = 5$

After trying out a few numbers we get $N_1 = 3$ and $N_2 =2$
$3*2 = 6$ , and $3 + 2= 5$

Factorising the expression:

$3x^2 +color(blue)( 5x) + 2 = 3x^2 + color(blue)(3x + 2x) + 2$

$= 3x(x + 1 ) + 2 ( x + 1 )$

$(x +1 )$ is a common factor to each of the terms

$=color(blue)((3x + 2 ) ( x + 1 )$

We now equate the factors to zero to obtain the solutions:

How do you factor and solve 3x^2+5x+2=03x^2+5x+2=0?