Solve the quadratic equation x^2+16=0 . Express its solutions in the form a±bi .(1 point)
To solve the quadratic equation x^2 + 16 = 0, we can rearrange the equation to isolate x^2:
x^2 = -16
To find the square roots of -16, we can express it as the product of its factors:
-16 = (-4)(4)
Now, using the imaginary unit i, we can express the square root of -1 as i:
√(-1) = i
Therefore, we can express the square root of -16 as √16 * √(-1) = 4i.
Finally, we can solve for x by taking the square root of both sides:
x = ±√(-16) = ±(4i)
The solutions to the quadratic equation are x = 4i and x = -4i.