If `alpha,beta` are the roots of `x^2+p x+q=0a n dgamma,delta` are the roots of `x^2+p x+r=0,` then `((alpha-gamma)(alpha-delta))/((beta-gamma)(beta-delta))=` a.`1` b. `q` c. `r` d. `q+r`

If alpha, beta be the roots of x^(2)+x+2=0 and gamma, delta be the roots of x^(2)+3 x+4=0 , then (alpha+gamma)(alpha+delta)(beta+gamma)(beta+delta) is equal to

If alpha,beta are roots of x^2+p x+1=0a n dgamma,delta are the roots of x^2+q x+1=0 , then prove that q^2-p^2=(alpha-gamma)(beta-gamma)(alpha+delta)(beta+delta) .

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

If alpha" and "beta are the roots of ax^(2)+bx+c=0 and alpha+k, beta+k are the roots of px^(2)+qx+r=0 , then (b^(2)-4ac)/(q^(2)-4pr)=

If alpha,beta are the roots of a x^2+b x+c=0a n dalpha+h ,beta+h are the roots of p x^2+q x+r=0then h= a. -1/2(a/b-p/q) b. (b/a-q/p) c. 1/2(b/a-q/p) d. none of these

If alpha, beta, gamma are the roots of 9x^3 - 7x + 6 = 0 , then alpha beta gamma is …………

If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' are the roots of x^(2) - p' x + q' = 0 , then the value of (alpha - alpha')^(2) + (beta + alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2) is

If alpha,beta are the roots of x^2-p x+q=0a n dalpha^(prime),beta' are the roots of x^2-p^(prime)x+q^(prime)=0, then the value of (alpha-alpha^(prime))^2+(beta-alpha^(prime))^2+(alpha-beta^(prime))^2+(beta-beta^(prime))^2 is a. 2{p^2-2q+p^('2)-2q^(prime)-p p '} b. 2{p^2-2q+p^('2)-2q^(prime)-q q '} c. 2{p^2-2q-p^('2)-2q^(prime)-p p '} d. 2{p^2-2q-p^('2)-2q^(prime)-q q '}

Let alpha,beta are the roots of x^2+b x+1=0. Then find the equation whose roots are - (alpha+1//beta)and-(beta+1//alpha) .

If alpha, beta are the roots of the equation (x-a)(x-b)=5 then the roots of the equation (x- alpha)(x-beta)+5=0 are