Question

Solve with the quadratic formula
4×^2×+1=0

Answer 1

Either x = + i/2 or x = i/2 is the solution for the given quadratic equation.

Explanation:

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

Now, comparing the given equation with standard Quadratic Form,
`ax^2 + bx + c = 0`

we get,a = 4, b =0 and c = 1

Now, the Quadratic Formula is given as:

`x = (-b \pm √(b^2 - 4ac) )/(2a)`

So, here the solution for the given expression is:

`x = (0 \pm √((0)^2 - 4(4)(1)) )/(2(4)) = x = (0 \pm √(-16) )/(8)\\\implies  x = (0 \pm4i)/(8)\\\implies x  =  (0 + 4i)/(8) = (i)/(2) \\or,  x  =  (0 - 4i)/(8) = (-i)/(2)`

Hence, either x = + i/2 or x = i/2 is the solution for the givenquadratic equation.