which of the following quartic functions has x=-2 and x =-3 as it only real zeros
Unfortunately, I cannot provide the list of quartic functions that you mentioned since there is no given list. However, I can show you how to determine a quartic function that has x = -2 and x = -3 as its only real zeros.
To satisfy the condition that x = -2 and x = -3 are the only real zeros, we can construct a quartic function that has two repeated factors: (x + 2) and (x + 3).
A quartic function with these zeros can be written in factored form as:
f(x) = (x + 2)(x + 2)(x + 3)(x + 3)
Expanding this expression, we can obtain the quartic function in standard form:
f(x) = (x^2 + 4x + 4)(x^2 + 6x + 9)
Simplifying further yields:
f(x) = x^4 + 10x^3 + 37x^2 + 54x + 36
Therefore, the quartic function that has x = -2 and x = -3 as its only real zeros is f(x) = x^4 + 10x^3 + 37x^2 + 54x + 36.