Mathematics

Problem

Determine the range of

p

for which the quadratic equation

3x^{2} + (2p - 1)x + (p + 4) = 0

has no real roots. a)

p < \dfrac{4 - \sqrt{63}}{2}\;\text{or}\;p > \dfrac{4 + \sqrt{63}}{2}

\dfrac{4 - \sqrt{63}}{2} \le p \le \dfrac{4 + \sqrt{63}}{2}

\dfrac{4 - \sqrt{63}}{2} < p < \dfrac{4 + \sqrt{63}}{2}

\dfrac{5 - \sqrt{69}}{4} < p < \dfrac{5 + \sqrt{69}}{4}