Final answer:
The difference is the polynomial obtained by subtracting the second polynomial from the first, resulting in 10x^4-12x^3+x^2+4x-7. The number of real zeros cannot be determined solely by this operation.
Step-by-step explanation:
To find the difference caused by subtracting one polynomial from another, we combine like terms. The given expressions are 7x^4−3x^3+5x^2−8x−11 and −3x^4+9x^3+4x^2−12x−4. Subtracting the second polynomial from the first, we get:
- (7x^4 - (-3x^4)) = 10x^4
- (-3x^3 - 9x^3) = -12x^3
- (5x^2 - 4x^2) = x^2
- (-8x - (-12x)) = 4x
- (-11 - (-4)) = -7
The resulting polynomial is 10x^4−12x^3+x^2+4x−7. Looking for the number of real zeros, it is important to note that the number of real zeros of a polynomial function can be determined by its degree and the sign changes in the coefficients. However, the original question's comparison to 'one real zero' is irrelevant to this process, as it cannot be determined without further analysis such as graphing the function or applying the Descartes' Rule of Signs.