Posted by **Candy** on Monday, June 3, 2013 at 9:57pm.

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

(i)Find the sum and product of its roots

(ii)show that 4m^2=25n

How to do part 2 ?

- amath -
**Reiny**, Monday, June 3, 2013 at 10:30pm
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!!!!

- amath -
**Candy**, Tuesday, June 4, 2013 at 1:52am
ohh I get it !! thanks a lot :))

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