# roots in m:n

the roots of $$ax^{2}$$+bx+c=0 ate in ratio m:n

let the roots be mk and nk respectively
=>a $$(mk)^{2}$$+bmk+c=0
=>a $$m^{2 } k^{2}$$+bmk+c=0.....(1)
Similarly,
a $$n^{2}$$$$k^{2}$$+bnk+c=0......(2)
(1)-(2)
=>a$$k^{2}$$($$m^{2 }$$-$$n^{2}$$)+bk(m-n)=0
=>a$$k^{2}$$(m+n)(m-n)+bk(m-n)=0
=>k(m-n)(ak(m+n)+b)=0
=>ak(m+n)+b=0
=>ak(m+n)=-b
=>k=-$$\frac {b}{a(m+n)}$$

therefore,
the roots are mk=-$$\frac{mb}{a(m+n)}$$
(or)
nk=-$$\frac{nb}{a(m+n)}$$

Note by Madhav Rockzz
2 years, 4 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

After letting one root be $$mk$$ and other be $$nk$$.

You could have directly used sum of roots = $$\dfrac{-b}{a}$$
$$\therefore k = \dfrac{-b}{a(m+n)}$$
Roots are,
$$\dfrac{-mb}{a(m+n)}$$ and $$\dfrac{-nb}{a(m+n)}$$

- 2 years, 4 months ago