Question

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

Answer 1

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:$4x^2 + 1 = 0$

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:

$x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}$

So, here the solution for the given expression is:

$x = \frac{0 \pm \sqrt{(0)^2 - 4(4)(1)} }{2(4)} = x = \frac{0 \pm \sqrt{-16} }{8}\\\implies x = \frac{0 \pm4i}{8}\\\implies x = \frac{0 + 4i}{8} = \frac{i}{2} \\or, x = \frac{0 - 4i}{8} = \frac{-i}{2}$

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