Question

If a and b are the roots of equation x²+px-q=0 and c, d are the roots of equation x²+px+r=0 then find out the answer of (a-c) (b-d) ​

Answer 1

Answer:

( a - c ) ( b - d ) = 2r - 2q - p²

Step-by-step explanation:

Since a and b are the roots of x²+px-q=0, we have

     a + b = -p   and   ab = -q.

Since c and d are the roots of x²+px+r=0, we have

     c + d = -p   and   cd = r.

Next we get

  p² = ( a + c ) ( b + d ) = ab + ad + bc + cd = ( ad + bc ) + r - q

so

  ad + bc = p² + q - r.

From here, we finally get

  ( a - c ) ( b - d )

= ab - ad - bc + cd

= r - q - ( ad + bc )

= r - q - ( p² + q - r )

= r - q - p² - q + r

= 2r - 2q - p²

Hope this helps!