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

3188 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

How does the photoelectric effect actually show that light is made up of particles?


A golf ball is hit at angle θ to the horizontal, with initial velocity u. Stating an assumption, show that the horizontal distance travelled by the ball is directly proportional to u^2.


Give a brief description of the Big Bang and describe its link to cosmic microwave background radiation.


How should I structure my experiment report?


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences