Answer:
[tex]0[/tex].
Step-by-step explanation:
Note that for [tex]p \ge 0[/tex], the expression [tex]p^{1/2}[/tex] is equivalent to [tex]\sqrt{p}[/tex]; additionally, [tex]p = \left(p^{1/2}\right)\, \left(p^{1/2}\right) = \left(\sqrt{p}\right)\, \left(\sqrt{p}\right)[/tex].
Rearrange the given equation and factorize:
[tex]p^{1/2} \, (5\, p^{1/2} + 4) = 0[/tex].
[tex]\sqrt{p} \, \left(5\, \sqrt{p} + 4\right) = 0[/tex].
By the Factor theorem, either:
However, since [tex]\sqrt{p} \ge 0[/tex] (the square root of a real number is non-negative,) it would not be possible for [tex](5\, \sqrt{p} + 4)[/tex] to be [tex]0[/tex]. Hence, the only possible way to satisfy the given equation is for [tex]\sqrt{p} = 0[/tex], such that [tex]p = 0[/tex].
