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.

AnswerscorrectIy Aug 9, 2024

#1**+1 **

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! :)

NotThatSmart Aug 9, 2024