Question

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

Answer 1

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

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

Explanation:

`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`