Question

If α and β are the zeroes of the quadratic polynomial f(x) = ax2 + bx + c, find the value of 1+ 1

Answer 1

Answer:

I can't understand what to do indiscretion in this situation

Answer 2

The quadratic polynomial

$ax {}^{2} + bx + c \: = f(x)$

a and ß are the zeros of an equation

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

and

$\alpha \beta = \frac{c}{a}$

$\frac{1}{ \alpha } - \frac{1}{ \beta } = \frac{ \beta - \alpha }{ \alpha \beta } = \frac{ - ( \alpha - \beta )}{ \alpha \beta }$

Consider ,

$(\alpha - \beta ) {}^{2} = ( \alpha + \beta ) {}^{2} + 4 \alpha \beta$

$( \alpha - \beta ) {}^{2} = ( \frac{ - b}{a} ) {}^{2} + \frac{4c}{a}$

$\alpha - \beta = \sqrt{ \frac{b {}^{2} }{a {}^{2} } + \frac{4c}{a} } = \frac{ \sqrt{b {}^{2} + 4ac } }{a}$

Therefore,

$\frac{1}{ \alpha } - \frac{1}{ \beta } = \frac{ - ( \alpha - \beta )}{ \alpha \beta } = \frac{ \frac{ \sqrt{b {}^{2} + 4ac } }{a} }{ \frac{c}{a} } = \frac{ \sqrt{b {}^{2} + 4ac } }{c}$

HOPE THIS WILL HELP YOU AND PLEASE MARK ME BRAINLIST