Question 151467
NO, it is NOT possible.
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Consider the quadratic equation:
{{{ (-b +- sqrt(b^2 - 4ac))/2a }}}
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Notice that we get our TWO solutions of a quadratic from the +- portion.
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Now, let's focus our attention on (the term after the +-):
{{{ sqrt(b^2 - 4ac) }}}
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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.