A negative number under the radical in quadratic equations?

Question

If I get a - under the radical what do I do?
x = 3 +/- sqrt -11 over 2
what do I do with the -11 under the radical?

Answer 1

you can not take a square root of a negative number, so in this case, there is no real solutions

However, you can use complex number
we know that sqrt(-1) = i

x = [3 +/- sqrt(-1 * 11)]/2
x = [3 +/- sqrt(-1) * sqrt(11)]/2
x = [3 +/- sqrt(11)i ]/2 <== complex solutions

Answer 2

x = (3 +/- i√11)/2

Since 11 is a prime number, your cannot factor it, also √(-1) = i
.

.