Question

if the α and β are the zeros of p (x) = ax^2+bx+ c so find the value of 1÷α+1÷β

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

If $\alpha \: \: and \: \: \beta \:$are the zeroes of the quadratic polynomial $a {x}^{2} + bx + c$

Then

$\displaystyle \: \alpha + \beta \: = - \frac{b}{a} \: \: and \: \: \: \alpha \beta \: = \frac{c}{a}$

GIVEN

$\alpha \: \: and \: \: \beta \:$are the zeroes of the quadratic polynomial $a {x}^{2} + bx + c$

TO DETERMINE

$\displaystyle \: \frac{1}{ \alpha } + \frac{1}{ \beta }$

CALCULATION

Since $\alpha \: \: and \: \: \beta \:$are the zeroes of the quadratic polynomial $a {x}^{2} + bx + c$

Then

$\displaystyle \: \alpha + \beta \: = - \frac{b}{a} \: \: and \: \: \: \alpha \beta \: = \frac{c}{a}$

So

$\displaystyle \: \frac{1}{ \alpha } + \frac{1}{ \beta }$

$= \displaystyle \: \frac{ \alpha + \beta }{ \alpha \beta }$

$= \displaystyle \: \frac{ - \frac{b}{a} }{ \frac{c}{a} }$

$= - \displaystyle \: \frac{ b }{ c }$

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ADDITIONAL INFORMATION

A general equation of quadratic equation is

$a {x}^{2} + bx + c = 0$

Now one of the way to solve this equation is by SRIDHAR ACHARYYA formula

For any quadratic equation

$a {x}^{2} + bx + c = 0$

The roots are given by

$\displaystyle \: x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a}$