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.

Answered by Andrew W. Physics tutor

2867 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

The friction coefficient of Formula 1 car tyres are around 1.7 in dry weather. Assuming sufficient power from the engine, calculate the theoretical best 0-100 km/h acceleration time in seconds. (neglect downforce, g=9.81m/s^2)


What are the differences between standing waves and progressive waves?


calculate the resistivity in a 1.2m length of cylindrical wire with radius 1cm. The resistance of the wire is 0.01 kilo Ohms


Describe the interaction that is responsible for keeping protons and neutrons together in a stable nucleus.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences