Mathematics

Problem

Determine the set of values of

k

for which the quadratic equation

x^{2}+2kx+(k+3)=0

has no real roots. a)

k<\dfrac{1-\sqrt{13}}{2}\;\text{or}\;k>\dfrac{1+\sqrt{13}}{2}

\dfrac{1-\sqrt{13}}{2}<k<\dfrac{1+\sqrt{13}}{2}

\dfrac{1-\sqrt{13}}{2}\le k\le\dfrac{1+\sqrt{13}}{2}

\dfrac{1-\sqrt{13}}{4}<k<\dfrac{1+\sqrt{13}}{4}