Home
Class 12
MATHS
If alpha and beta are the roots of x...

If ` alpha and beta ` are the roots of ` x^(2) +px+q=0` and ` gamma , delta `are the roots of ` x^(2) +rx+x=0` , then evaluate `(alpha - gamma ) ( beta - gamma ) (alpha - delta ) ( beta - delta) ` in terms of p,q,r and s .

Text Solution

Verified by Experts

The correct Answer is:
`(q-s)^2-rpq-rsp+sp^(2)+qr^(2) `
Promotional Banner

Similar Questions

Explore conceptually related problems

If alpha and beta are the roots of x^(2) +px+q=0 and gamma, delta are the roots of x^(2)+rx+s=0, then evaluate (alpha-gamma)(beta-gamma) (alpha-delta) (beta-deta) in terma of p,q, r and s.

If alpha and beta are the roots of the equation x^(2) +px+1=0 , gamam , delta are the roots of (x^(2) +qx+1=0 , then , find ( alpha-gamma ) (beta - gamma ) ( alpha + delta )(beta + delta )

If alpha and beta are the roots of quadratic equation x^(2)+px+q=0 and gamma and delta are the roots of x^(2)+px-r=0 then (alpha-gamma)(alpha-delta)

If alpha,beta are roots of x^(2)+-px+1=0 and gamma,delta are the roots of x^(2)+qx+1=0 ,then prove that q^(2)-p^(2)=(alpha-gamma)(beta-gamma)(alpha+delta)(beta+delta)

If alpha, beta are the roots of quadratic equation x^(2)+px+q=0 and gamma, delta are the roots of x^(2)=px+r=0, then (alpha-gamma).(alpha-delta) is equal to

If alpha,beta are the roots of x^(2)+ax-b=0 and gamma,delta are the roots of x^(2)+ax+b=0 then (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta)=

If alpha,beta are the roots of x^(2)+px+q=0and gamma,delta are the roots of x^(2)+rx+s=0, evaluate (alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta) in terms of p,q,r, ands.Deduce the condition that the equation has a common root.