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

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Answer 1 · 2016-05-24T15:29:42

The solutions for the equation are

$x = - \frac{2}{3}$ $color(green)(x = -2/3$

$x = - 1$ $color(green)(x = -1$

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

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $a x^{2} + b x + c$ $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 3 \cdot 2 = 6$ $N_1*N_2 = a*c = 3*2 = 6$

AND

$N_{1} + N_{2} = b = 5$ $N_1 +N_2 = b = 5$

After trying out a few numbers we get $N_{1} = 3$ $N_1 = 3$ and $N_{2} = 2$ $N_2 =2$
$3 \cdot 2 = 6$ $3*2 = 6$ , and $3 + 2 = 5$ $3 + 2= 5$

Factorising the expression:

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

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

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

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

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

How do you factor and solve 3x^2+5x+2=03x2+5x+2=03x^2+5x+2=0?