Question

What is the factored form of the expression?

16x^2 + 24x + 9

Answer 1

`(x+(3)/(4))(x+(3)/(4))=0`

Explanation:

We are given the quadratic equation
`16x^(2)+24x+9=0`

Now, the roots of the quadratic equation
`ax^(2)+bx+c=0` are given by
`x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}`.

So, from the given equation, we have,

a = 16, b =24 , c = 9.

Substituting the values in
`x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}`, we get,

`x=\frac{-24\pm \sqrt{(24)^(2)-4* 16* 9}}{2* 16}`

i.e.
`x=(-24\pm √(576-576))/(32)`

i.e.
`x=(-24\pm √(0))/(32)`

i.e.
`x=(-24)/(32)`

i.e.
`x=(-3)/(4)`

Thus, the roots of the equation are
`(-3)/(4)` and
`(-3)/(4)`.

Hence, the factored form of the given expression will be
`(x+(3)/(4))(x+(3)/(4))=0`