Posted by **Jayden Haddy** on Saturday, August 17, 2013 at 6:01am.

If the ratio of the roots of the quadratic equation ax^2 + bx +c =0 is m:n

prove that mnb^2=(m+n)^2 ac

- maths -
**Sasuke**, Saturday, August 17, 2013 at 6:34am
sum: m + n = -b/a

product: mn = c/a

substitute. when proving, you only manipulate/solve one side.

mnb^2=(m+n)^2 ac

(c/a)(b^2) =? (ac)(m+n)^2

(c/a)[a(m + n)]^2 =? (ac)(m+n)^2

(c/a)(a^2)(m+n)^2 =? (ac)(m+n)^2

(ac)(m+n)^2 = (ac)(m+n)^2

this problem is pretty much the same as the one you posted earlier. you should also check Naruto's answer on that post.

- maths -
**Writeacher**, Saturday, August 17, 2013 at 10:25am
Gee! Naruto and Sasuke seem to be the same person!!

## Answer This Question

## Related Questions

- maths - If the sum of the squares of the roots of the quadratic equation ax^2 + ...
- Math - If the roots of the quadratic equation ax^2+bx+c=0 are in the ratio r:1 ...
- maths -quadratic eqn - one of the roots of the quadratic equation x^2-(4+k)x+12=...
- Math (Algebra) - If the ratio of the roots of the quadratic equation x^2−...
- maths - Given that a and b are the roots of the quadratic equation 2x^2 - 4x +3...
- Math - I can't remember how you find the roots of quadratic equations other than...
- 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...
- maths - Prove that if p and q are rational and p is not equal to 0, the roots ...
- Add maths form 4 - Given that the quadratic equation hx^2 - 4kx + 9h =0 has two ...

More Related Questions