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 :))

## Answer This Question

## Related Questions

- Algebra - Given the roots, 1/2 and 4, find: (A) The quadratic equation 2x^2-9x+4...
- Precalculus - "Show that x^6 - 7x^3 - 8 = 0 has a quadratic form. Then find the ...
- Math - I can't remember how you find the roots of quadratic equations other than...
- Math (Algebra) - If the ratio of the roots of the quadratic equation x^2−...
- maths -quadratic eqn - one of the roots of the quadratic equation x^2-(4+k)x+12=...
- maths-equadratic eqn - one of the roots of the quadratic equation x^2-(4+k)x+12=...
- Algebra2 - Find the polynomials roots to each of the following problems: #1) x^2...
- Math - I can't seem remember the rules for this.Can someone please help me with ...
- Alg 2 - By what amount does the sum of the roots exceed the product of the roots...
- algebra - if a quadratic equation with real coefficents has a discriminant of 10...

More Related Questions