X^4-17x^3+15x^2+17x-16=0

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To solve this quartic equation, we can use either numerical methods or factorization techniques. Here, we will attempt to factorize the equation.

Given equation: x^4 - 17x^3 + 15x^2 + 17x - 16 = 0

We can see that this equation does not have any common factor among its terms, so we need to find its roots using factorization techniques or by using a numerical method like the Newton-Raphson method or the bisection method.

Let's assume that the equation can be factored as:

(x^2 + Ax + B)(x^2 + Cx + D) = 0

Expanding the above equation, we get:

x^4 + (A+C)x^3 + (AC+B+D)x^2 + (AD + BC)x + BD = 0

By comparing the coefficients of the given equation with the expanded form above, we get:

A + C = -17
AC + B + D = 15
AD + BC = 17
BD = -16

Now, we need to find suitable values for A, B, C, and D that satisfy the above conditions.

By trial and error or by solving the above system of equations, we can find the values of A, B, C, and D. Once we have those values, we can factorize the equation and find its roots.

Note: Factoring a quartic equation can be more complex and may not always lead to rational roots. In such cases, numerical methods may be a better option.