How do you solve $4x^2+8x+3$ ?

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Answer 1 · 2015-08-19T06:21:21

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

$color(blue)(x=-1/2$

$4x^2+8x+3$ , solving assuming that the expression is equated to zero.

$4x^2+8x+3=0$

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:

$N_1*N_2 = a*c = 3*4 = 12$
and
$N_1 +N_2 = b = 8$

After trying out a few numbers we get $N_1 = 2$ and $N_2 =6$
$2*6 = 12$ , and $2+6= 8$

$4x^2+8x+3 = 4x^2+2x+6x+3$

$4x^2+2x+6x+3 = 2x(2x+1) +3(2x+1)$

$(2x+3)(2x+1)=0$

Now we equate factors to zero.
$2x+3=0, color(blue)(x=-3/2$

$x+2=0,color(blue)(x=-1/2$

How do you solve 4x^2+8x+34x^2+8x+3?