Answer:

Heya!!Here is your answer friend ⤵⤵

\begin{gathered}an \: equation \: has \: no \: real \: roots \: when \\ \sqrt{b {}^{2} - 4c } < 0 \\ here \\ \sqrt{b {}^{2} - 4ac } = \sqrt{12 {}^{2} - 4 \times 4 \times 15 } \\ = \sqrt{144 - 4 \times 60} \\ \sqrt{144 - 240} = \sqrt{ - 96} \end{gathered}

anequationhasnorealrootswhen

b

2

−4c

<0

here

b

2

−4ac

=

12

2

−4×4×15

=

144−4×60

144−240

=

−96

This value is less than zero. Hence it has no real roots