Question

find and explain the solution​

Answer 1

The given equality can be proven as follows

1) The ratio of roots is m:n, let the roots of equation be mz and nz.

2) product of roots is $\alpha *\beta = c/a$

mz*nz = c/a  

mnz² = c/a  -------->(1)

3) Sum of roots is $\alpha + \beta = -b/a$

mz+nz = -b/a --------->(2)

squaring both sides (m+n)z² = b²/a²

4) dividing equation 1 from 2

$\frac{mnz^{2} }{(m+n)z^{2} } = \frac{c}{a} * \frac{a^2}{b^2}$

5) Solving and arranging :- mnb² = (m+n)²ac