Mathematics

Problem

Suppose a quadratic polynomial has zeros such that one zero is exactly twice the other. a. (i) If the quadratic is written in the general form

ax^{2}+bx+c

, derive a relation among

a,\,b

and

c

that represents the given condition on its zeros. b. (ii) The polynomial

t^{2}-9t+d

satisfies the above condition. Find the value of

d

. c. (iii) For this value of

d

, find both zeros of the polynomial and verify that one is indeed twice the other.