Answer:
The solution for the given polynomial [tex]4x^2 + 4x+ 1 = 0[/tex] is [tex]x = (\frac{-1}{2})[/tex]
Step-by-step explanation:
Here, the given quadratic equation is : [tex]4x^2 + 4x+ 1 = 0[/tex]
Now, here solving the given equation by SPLITTING THE MIDDLE TERM:
[tex]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\\[/tex]
⇒ 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 [tex]4x^2 + 4x+ 1 = 0[/tex] is [tex]x = (\frac{-1}{2})[/tex]
