Answer:
No real zeros.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Discriminant of the Quadratic Formula}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\When $b^2-4ac > 0 \implies$ two real zeros.\\When $b^2-4ac=0 \implies$ one real zero.\\When $b^2-4ac < 0 \implies$ no real zeros.\\\end{minipage}}[/tex]
The value of the discriminant shows how many zeros the function has.
Given quadratic function:
[tex]f(x)=5x^2+5x+21[/tex]
Therefore:
Substitute the values into the discriminant and solve:
[tex]\begin{aligned}\implies b^2-4ac&=(5)^2-4(5)(21)\\& = 25 - 20(21)\\&=25-420\\&=-395\end{aligned}[/tex]
Therefore, as -395 < 0, there are no real zeros.
