Question

Find the solutions to the equation below.
Check all that apply.
4x2 + 4x + 1 = 0

Answer 1

The solution for the given polynomial
`4x^2 + 4x+ 1 = 0` is
`x  = ((-1)/(2))`

Explanation:

Here, the given quadratic equation is :
`4x^2 + 4x+ 1 = 0`

Now, here solving the given equation by SPLITTING THE MIDDLE TERM:

`4x^2 + 4x+ 1 = 0  = 4x^2 + 2x+ 2x +  1 = 0\\\implies 2x( 2x + 1) + 1(2x + 1) = 0\\\implies (2x +1)(2x +1)  = 0\\`

⇒ either (2x+1) = 0, or ( 2x + 1) = 0

⇒ x = -1/2 or x = -1/2

Here, in both the cases, the value of x is equal i.e x = -1/2

So, the given function has TWO IDENTICAL ROOTS.

Hence the solution for the given polynomial
`4x^2 + 4x+ 1 = 0` is
`x  = ((-1)/(2))`