+617 For what real values of k does the quadratic 12x^2 + kx + 27 = 8x^2 + 18 + 14x^2 + 32 have nonreal roots? Enter your answer as an interval.
+1798 First, let's move all terms to one side and set up a quadratic equation. We have
\(-10x^2+kx-23=0\)
Now, in order for the roots to be nonreal, the descriminant must be less than 0. Thus, we can write the equation
\(k^2-920 < 0\)
Now, we simply solve for k. We have
\(k^2<920\\ \)
Since we must square k, there are two restrictive intervals for k. We have
\(-2\sqrt{230} <2\sqrt{230}\)
So our final answer for k is
\(-2\sqrt{230} <2\sqrt{230}\)
Thanks! :)
