Answer:
Irrational
Step-by-step explanation:
[tex]f(x) = 2 {x}^{2} - 3x - 8 \\ equating \: it \: with \\ f(x) = a {x}^{2} + bx + c \\ a = 2 \: \: b = - 3 \: \: c = - 8 \\ {b}^{2} - 4ac \\ = ( - 3)^{2} - 4 \times 2( - 8) \\ = 9 + 64 \\ = 73 \\ \because \: 73 \: is \: not \: a \: perfect \: square \: no \\ \therefore \: \sqrt{73} \: is \: irrational[/tex]
Hence, given function has irrational roots.
