(a) (b) Prove that log, 5 is irrational Suppose that a and b are real numbers...

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(a) (b) Prove that log, 5 is irrational Suppose that a and b are real numbers where b# 0 Consider the polynomial P(z)=z¹ + az² + b The polynomial has a double root at z = a (i) Show that P'(z) is an odd function. Show that - a is also a double root a² E (iii) (iv) ((v)) Prove that b = For what value(s) of a does P(z) have double root equal to √3i For what values of a does P(z) have Real roots? (a) (b) Prove that log, 5 is irrational Suppose that a and b are real numbers where b# 0 Consider the polynomial P(z)=z¹ + az² + b The polynomial has a double root at z = a (i) Show that P'(z) is an odd function. Show that - a is also a double root a² E (iii) (iv) ((v)) Prove that b = For what value(s) of a does P(z) have double root equal to √3i For what values of a does P(z) have Real roots?

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a Log 5 is irrational if it is rational that is if it can be written as a fraction in the simplest f... View the full answer