Question

if the roots of the equation (q-r)x^2+(r-p)x+p-q=0, then show that p,q and r are in AP​.

Answer 1

Answer:  let, if the root is =alpha and beta  ($\beta \alpha$)                                                                                            

               

Step-by-step explanation:

(q-r)x^2+(r-p)x+p-q=0                            let putting x=1

=> q-r+r-p+p-q=0                                  so,1 is first root of this equation($\alpha$=1)

=> so, $\alpha \beta$=c/a

=> 1*$\beta$=c/a                                             so, c=p-q and a =q-r

=>$\beta$=p-q/q-r

so, root are 1 and p-q/q-r