SOLUTION: I am having trouble understanding if some quadratic equations can have one real and one imaginary solution? Is that possible?

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Question 151467: I am having trouble understanding if some quadratic equations can have one real and one imaginary solution? Is that possible?

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
NO, it is NOT possible.
.
Consider the quadratic equation:
+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a+
.
Notice that we get our TWO solutions of a quadratic from the +- portion.
.
Now, let's focus our attention on (the term after the +-):
+sqrt%28b%5E2+-+4ac%29+
.
Notice that if:
4ac is greater than b^2 then we will have to take the square root of a NEGATIVE number -- creating an imaginary solution. Once this is the case BOTH solutions will be imaginary.