The roots of the quadratic equation x^2-mx+n=0 ,where m and n are integers ,are a and 1/4a.

Question

(i)Find the sum and product of its roots
(ii)show that 4m^2=25n

How to do part 2 ?

Answer 1

You must be studying the property of the roots of a quadratic, where
sum of roots = -b/a
product of roots = c/a

so for x^2 - mx + n
the sum of the roots = m
product of the roots = n

but you are given the roots as a and 1/4a
sum of roots = a + 1/4a = (5/4)a
product of roots = (1/4)a^2

so (5/4)a = m --- >a = 4m/5 or a2 = 16m^2/25
(1/4)a^2 = n --- a^2 = 4n

thus: 16m^2/25 = 4n
16m^2 = 100n
4m^2 = 25n

Voila!!!!

Answer 2

ohh I get it !! thanks a lot :))