Answer:
a = 3, b = 2
Step-by-step explanation:
It is given that both the polynomials are equal.
Therefore, h(x) = k(x)
[tex] {x}^{3} + (a + b) {x}^{2} - 4x + 2 \\ = {x}^{3} + 5 {x}^{2} - (2a - b)x + 2 \\ \\ equating \: like \: terms \: on \: both \: sides \\ (a + b) {x}^{2} = 5 {x}^{2} \\ \implies \: a + b = 5.....(1) \\ \\ - (2a - b)x = - 4x \\ 2a - b = 4....(2) \\ \\ adding \: equations \: (1) \: and \: (2) \\ \\ 3a = 9 \\ \implies \: a = \frac{9}{3} \\ \huge \red{ \boxed{\implies \: a = 3}} \\ \\ substituting \: a = 3 \: in \: equation \: (1) \\ 3 + b = 5 \\ \implies \: b = 5 - 3 \\ \huge \purple{ \boxed{ \implies b = 2}}[/tex]
