which of the following quartic functions has x=-2 and x =-3 as it only real zeros?
A) x^4-5x^3+7x^2-5x-6
B) x^4-5x^3+7x^2+5x+6
C) x^4-5x^3+7x^2-5x+6
D) x^4-5x^3+7x^2+5x-6
To determine which quartic function has x=-2 and x=-3 as its only real zeros, we need to substitute these values into each function and check if the result is equal to zero.
A) (-2)^4-5(-2)^3+7(-2)^2-5(-2)-6 = 16+40+28+10-6 = 88
(-3)^4-5(-3)^3+7(-3)^2-5(-3)-6 = 81+135+63+15-6 = 288
B) (-2)^4-5(-2)^3+7(-2)^2+5(-2)+6 = 16+40+28-10+6 = 80
(-3)^4-5(-3)^3+7(-3)^2+5(-3)+6 = 81+135+63-15+6 = 270
C) (-2)^4-5(-2)^3+7(-2)^2-5(-2)+6 = 16+40+28+10+6 = 100
(-3)^4-5(-3)^3+7(-3)^2-5(-3)+6 = 81+135+63+15+6 = 300
D) (-2)^4-5(-2)^3+7(-2)^2+5(-2)-6 = 16+40+28-10-6 = 68
(-3)^4-5(-3)^3+7(-3)^2+5(-3)-6 = 81+135+63-15-6 = 258
Out of the four options, only option B) results in zero when substituting x=-2 and x=-3. Therefore, the correct answer is option B) x^4-5x^3+7x^2+5x+6.