Question

Does the equation shown have rational or irrational solutions?

Answer 1

Irrational

Explanation:

`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 * 2( - 8) \\ = 9 + 64 \\ = 73 \\ \because \: 73 \: is \: not \: a \: perfect \: square \: no \\ \therefore \: √(73) \: is \: irrational`

Hence, given function has irrational roots.

Answer 2

hope it helps you see the attachment for further information..... \