Question

find all rational roots of h(x).
h(x) = -x⁴ + 16x³ - 50x² - 56x + 11
write your answer as a list of simplified values separated by commas, if there is more than one value.

Explanation:

Step1: Apply Rational Root Theorem

Possible rational roots are $\pm1, \pm11$.

Step2: Test $x=1$

$h(1) = -(1)^4 + 16(1)^3 - 50(1)^2 - 56(1) + 11 = -1 + 16 - 50 - 56 + 11 = -80
eq 0$

Step3: Test $x=-1$

$h(-1) = -(-1)^4 + 16(-1)^3 - 50(-1)^2 - 56(-1) + 11 = -1 -16 -50 +56 +11 = 0$

Step4: Test $x=11$

$h(11) = -(11)^4 + 16(11)^3 - 50(11)^2 - 56(11) + 11$
$= -14641 + 20596 - 6050 - 616 + 11 = -700
eq 0$

Step5: Test $x=-11$

$h(-11) = -(-11)^4 + 16(-11)^3 - 50(-11)^2 - 56(-11) + 11$
$= -14641 - 20596 - 6050 + 616 + 11 = -40660
eq 0$

Step6: Verify no other rational roots

Since all possible candidates are tested, only $x=-1$ is a rational root.

Answer:

$-1$