Question

1

Answer 1

use rational root test which is a trial and error method. you use x's that are factors of the last term (-6) and the first term (4)

so 1,-1,2,-2,4,-4 whichare the factors of 4 and 1,-1,2,-2,3,-3,6,-6 which are the factors of 6. So we try each one, see if it gives 0.

Try 1, we see 4-5+9-6 is not 0
Try -1 we get 4(-1)^3 - 5(-1)^2 + 9(-1) + 6= -4 -5 -9 + 6 again not 0
Try 2 we get 4(2)^3 - 5(2)^2 + 9(2) - 6= 32-20+18-6 again not 0
Try -2 we get 4(-2)^3-5(-2)^2+9(-2)-6= -32-20 -18-6 which isnot 0
Try 3, we get 4(3)^3-5(3)^2+9(3)-6= 108-45+27-6 not 0
Try -3 again doesnt give 0
Try 4 again not 0
Try -4 again not 0

Try pluging all values till 6 and -6, it doenst look like this function have rational zeros.