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
Related Physics A Level answers
All answers ▸An object is let in free fall from a platform 20m high above Earth's surface. Describe the event in terms of energy and thus determine the speed of the object when it hits ground. Air resistance is negligible and gravitational acceleration is constant.
Why do skydivers have a terminal velocity?
"An inclined plane at an angle of 25 degrees to the horizontal has a pulley at its top. A 30kg block on the plane is connected to a freely hanging 20kg block by means of a cord passing over the pulley. From rest how far will the 20kg block fall in 2s?
The flow of water in a pipe is turbulent. Define turbulent flow.