amath

posted by .

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 -

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 -

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

Similar Questions

1. Algebra2

Find the polynomials roots to each of the following problems: #1) x^2+3x+1 #2) x^2+4x+3=0 #3) -2x^2+4x-5 #3 is not an equation. Dod you omit "= 0" at the end?
2. Precalculus

"Show that x^6 - 7x^3 - 8 = 0 has a quadratic form. Then find the two real roots and the four imaginary roots of this equation." I used synthetic division to get the real roots 2 and -1, but I can't figure out how to get the imaginary …
3. Algebra

Given the roots, 1/2 and 4, find: (A) The quadratic equation 2x^2-9x+4 ?
4. Alg 2

By what amount does the sum of the roots exceed the product of the roots of the equation (x-7)(x+3)=0?
5. Math (Algebra)

If the ratio of the roots of the quadratic equation x^2−28x+A=0 is 2:5, what is the product of the roots of the quadratic equation x^2+Ax+2A+3=0?

7. Math

I can't remember how you find the roots of quadratic equations other than determining the zeroes of the equation and finding the x-intercepts. Can someone please give me a clear answer on this as my dad has been useless on this topic …
8. algebra

if a quadratic equation with real coefficents has a discriminant of 10, then what type of roots does it have?