Find all rational zeros of the polynomial, and then find the irrational zeros, if any. Whenever appropriate, use the Rational Zeros Theorem, the Upper and Lower Bounds Theorem, Descartes' Rule of Signs, the Quadratic Formula, or other factoring techniques.

Rationals zeros 1, -2, 3/4

Irationals zeros

Step-by-step explanation:

The factors of 6 are: -1,1,-2,2,-3,3,-6,6.

The cactors of 8 are: -1,1,-2,2,-4,4,-8,8.

The possible rationals zeros for P(x) are: -1,1,1/2,-1/2,-1/4,1/4,-1/8,1/8,-2,2,-3,3,-3/2,3/2,-3/4,3/4,-3/8,3/8,-6,6.

For all possible rational zeros for P(x), we check is it P(rat.zero)=0?

You can see that

Now we have that

In the same way we can see:

Apply the quadric formula:

we get and .

8

step-by-step explanation: