Question

For what real values of $k$, other than $k=0$, does the equation $x^2+kx+k^2=0$ have real roots? (The symbol $x\ge a$ means that $x$ can take on all values greater than $a$ and the value $a$ itself; $x\le a$ has the corresponding meaning with "less than")

• A. $k<0$
• B. $k>0$
• C. $k\ge 1$
• D. all values of $k$
• E. no values of $k$

Answer 1

Answer: (E)

no values of $k$

$x=\frac{-k\pm \sqrt{k^2-4k^2}}{2}$ For $x$ to be real, $k^2-4k^2\ge 0$, an impossibility.