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------------------------------------------------ Define the polynomial [tex]f(x) = x^5 + 3x^4 - 4x^3 + 59x^2 - 75x + 35[/tex] and find the roots of the polynomial.

Answer :

Final answer:

To find the roots of the polynomial f(x)=x⁵+3x⁴-4x³+59x²-75x+35, write the polynomial in descending order and use the Roots command in a calculator or mathematical software.

Explanation:

To find the roots of a polynomial, we need to solve the equation f(x) = 0. In this case, the polynomial is f(x) = x⁵+3x⁴-4x³+59x²-75x+35. To find the roots, we can use the Roots command.

  1. Write the polynomial in descending order.
  2. Use the Roots command in your calculator or mathematical software to find the roots of the polynomial.

In this case, the roots of the polynomial are -7, -1, -1, 1, and 5.

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