Question

Date :
if the zeros of polynomial ax^2+bx+c
are
alpha and ß then find the zeros
of polynomial cx^2 - 2bx+ 4a including
& and ß​

Answer 1

Step-by-step explanation:

Let,

z be the general zero of ax²+bx+c i.e.

$z = \alpha \: or \beta$

Then,

az²+bz+c=0

Let,

$z = - \frac{2}{y}$

Then,

$a( - \frac{2}{y})^{2} + b( - \frac{2}{y}) + c = 0$

Multiplying both side by y²

$4a - 2by + cy^{2} = 0$

$= cy^{2} - 2by + 4a = 0$

But this is the equation whose roots we are looking for.

We observe that y is the general solution of this equation.

But y= -2/z

But

$z = \alpha \: or \beta$

Therefore

$y = - \frac{2}{ \alpha } \: or \: - \frac{2}{ \ \beta }$

This is the required solution.