Final answer:
To find a quartic equation with the given expression, we need four terms. We can add two more terms involving x⁴ and x³ to create the quartic equation.
Step-by-step explanation:
In order to find a quartic equation, we need four terms. The given expression, x²-8x+11x²-4x-5, only has two terms. To create a quartic equation, we can add two more terms that involve x⁴ and x³.
Let's assign the variables a, b, c, and d to the coefficients of x⁴, x³, x², and x, respectively. The equation becomes:
a*x⁴ + b*x³ + (1+11)*x² + (-8-4)*x + (-5) = 0
Simplifying it further:
a*x⁴ + b*x³ + 12x² - 12x - 5 = 0
So, a quartic equation with the given expression is a*x⁴ + b*x³ + 12x² - 12x - 5 = 0.