Answer:
Either x = + i/2 or x = i/2 is the solution for the given quadratic equation.
Step-by-step explanation:
Here, the given quadratic equation is:[tex]4x^2 + 1 = 0[/tex]
Now, comparing the given equation with standard Quadratic Form, [tex]ax^2 + bx + c = 0[/tex]
we get,a = 4, b =0 and c = 1
Now, the Quadratic Formula is given as:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
So, here the solution for the given expression is:
[tex]x = \frac{0 \pm \sqrt{(0)^2 - 4(4)(1)} }{2(4)} = x = \frac{0 \pm \sqrt{-16} }{8}\\\implies x = \frac{0 \pm4i}{8}\\\implies x = \frac{0 + 4i}{8} = \frac{i}{2} \\or, x = \frac{0 - 4i}{8} = \frac{-i}{2}[/tex]
Hence, either x = + i/2 or x = i/2 is the solution for the givenquadratic equation.
