Final answer:
To solve the combined polynomial (x² - 4x - 1) + (-5 + 5x² - 3x), like terms are added together, resulting in the quadratic equation 6x² - 7x - 6.
Step-by-step explanation:
The question asks to solve the combined polynomial (x² - 4x - 1) + (-5 + 5x² - 3x). First, we need to combine like terms. This involves adding the coefficients of the corresponding powers of x. The term with x² in the first polynomial has a coefficient of 1, and in the second polynomial, a coefficient of 5, so when combined, the x² term has a coefficient of 1 + 5 = 6. The term with x in the first polynomial has a coefficient of -4, and in the second polynomial, a coefficient of -3, so combined, the x term has a coefficient of -4 - 3 = -7. The constant terms are -1 and -5, so combined, they make -1 - 5 = -6.
The combined polynomial is therefore 6x² - 7x - 6. This is a quadratic equation and could be solved using the quadratic formula or by factoring if possible. However, the question does not specifically ask for the roots of this equation; it simply asks for the equation to be combined.