Question 1209700
To find the roots of the polynomial f(x) = x^4 - 5x^3 + 5x^2 + 17x - 42 + 4x^4 + 10x^3 - 18x^2 + 2x - 5, we first need to combine the like terms to simplify the polynomial.

Combining the x^4 terms: x^4 + 4x^4 = 5x^4
Combining the x^3 terms: -5x^3 + 10x^3 = 5x^3
Combining the x^2 terms: 5x^2 - 18x^2 = -13x^2
Combining the x terms: 17x + 2x = 19x
Combining the constant terms: -42 - 5 = -47

So, the simplified polynomial is:
f(x) = 5x^4 + 5x^3 - 13x^2 + 19x - 47

To find the roots of this quartic polynomial, we can use numerical methods or a computer algebra system. The roots are approximately:

x ≈ -2.81952163
x ≈ 1.56441331
x ≈ 0.12755416 + 1.45424058i
x ≈ 0.12755416 - 1.45424058i

These are the four roots of the polynomial. Two are real, and two are complex conjugates.