Question

Please please please



if a, ß are the zeros of the polynomial f(x) = ax2 + bx + c then 1/alpha² + 1/beta²​

Answer 1

Step-by-step explanation:

here is your answer mate hope it helps you

Answer 2

Answer:

Given:

α and β are the roots of the the polynomial given as follows:

ax² + bx + c = 0

To find:

Value of

$\frac{1}{ { \alpha }^{2} } + \frac{1}{ { \beta }^{2} }$

Calculation:

We know that :

$1. \: \alpha + \beta = - \frac{b}{a}$

$2. \: \alpha \times \beta = \frac{c}{a}$

As per the question:

$\frac{1}{ { \alpha }^{2} } + \frac{1}{ { \beta }^{2} }$

$= \frac{ { \alpha }^{2} + { \beta }^{2} }{ { (\alpha \beta ) }^{2} }$

$= \frac{ {( \alpha + \beta )}^{2} - 2 \alpha \beta }{ {( \alpha \beta )}^{2} }$

Now putting values :

$= \frac{ { ( - \frac{b}{a} )}^{2} - 2 \times (\frac{c}{a} )}{ {( \frac{c}{a}) }^{2} }$

$= \frac{ \frac{ {b}^{2} - 2ac}{ {a}^{2} } }{ { (\frac{c}{a}) }^{2} }$

$= \frac{ {b}^{2} - 2ac}{ {c}^{2} }$

This is the final answer.