If the quadratic equations x^2 + px + q = 0 and x^2+ p' x + q' = 0 have a common root . Show that it must be either ( p q' - p' q / q - q' ) or   ( q - q' / p' q )

Solⁿ:

Let α be the common root of the given equations:

α2 + pα + q = 0 …(i)

and α2 + p’α + q’ = 0 …(ii)

Solving (i) and (ii) by cross multiplication,

1              p             q                  1

1              p’            q’                 1

Or, α²/(pq′p′q) = α/(qq′) =...

Solve:dy/dx = cos(x+y)

Mention two alternatives sources of energy .