How is x square - ( sum of zeroes )x +( product of zeroes ) , the general form of a quadratic equarion?? Sum of zeroes is - b by a so how is it the general form of a quadratic equation. This is the reply of the answer fiven by a expert in my precious question.. Plz mam/ sir,, i dont understand the concept clearly. Help me ro understand the values of alfa and beta and when to use it. Plz hepl me understand!!. Plz see this question again show how it is the general form.

Dear Student,

Please find below the solution to the asked query:

Let we have two zeroes of quadratic equation  = $\mathrm{\alpha }$ and $\mathrm{\beta }$  (  We assume zeroes of quadratic equation  $\mathrm{\alpha }$ and $\mathrm{\beta }$ when zeros not given )

Then . Quadratic equation we get  :

( x  - $\mathrm{\alpha }$ ) ( x  - $\mathrm{\beta }$ )

$\Rightarrow$x² - $\mathrm{\beta }$ x  -  $\mathrm{\alpha }$ x  + $\mathrm{\alpha }$ $\mathrm{\beta }$ 

$\Rightarrow$x² - ( $\mathrm{\alpha }$  + $\mathrm{\beta }$ ) x  + $\mathrm{\alpha }$ $\mathrm{\beta }$ 

$\Rightarrow$x² - ( Sum of zeroes ) x  + ( Product of zeroes )                 ( As we can see that  $\mathrm{\alpha }$  + $\mathrm{\beta }$ =  Sum of zeroes  and $\mathrm{\alpha }$ $\mathrm{\beta }$ = Product of zeroes  )

Thats our required equation ( or formula to get quadratic equation when zeroes are given )

We know general quadratic equation :  a x² + b x  +  c =  0 

And if we assume zeroes of quadratic equation  = $\mathrm{\alpha }$ and $\mathrm{\beta }$  , Then

Sum of zeroes  = $\mathrm{\alpha }$ + $\mathrm{\beta }$  = $-\frac{\mathrm{b}}{\mathrm{a}}$

And

Product of zeroes  =  $\mathrm{\alpha }$ $\mathrm{\beta }$  = $\frac{\mathrm{c}}{\mathrm{a}}$

Hope this information will clear your doubts about topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards