Given that z = 6 is a root of the cubic equation z^3 − 10z^2 + 37z + p = 0, find the value of p and the other roots.
Okay, first, we will tackle this by using the information given to us (z=6) to solve for p. By substituting 6 wherever there is a z, we will end up with 216 - 360 + 222 + p = 0.Solving this through rearrangement leaves us with p = -78. Then, we can use the factor theorem. If z=6 is a root, then (z-6) is a factor, so then we can use factor division to find the other two factors, and thus, the remaining roots of the equation.
AW
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