If a and b are the roots of `x^2 – 3x + p = 0` and c, d are roots of `x^(2) – 12x + q = 0` , where a,b,c,d form a G.P Prove that (q+q):(q-p) = 17 : 15

If p and q are the roots of the equation x^2-p x+q=0 , then

If alpha, beta are the rots of a x^(2)+b x+c=0 and alpha+h, beta+h are the roots of p x^(2)+q x+r=0 then h=

If p and q are the roots of the equation x^(2)+p x+q=0 then

Let alpha, beta be the roots of x^(2) -x + p = 0 and gamma , delta be the roots of x^(2) - 4x + q = 0 . If alpha, beta, gamma , delta are in G.P., then the integral value sof p and q respectively, are :

If p and q are the roots of the equations x^(2) - 3x+ 2 = 0 , find the value of (1)/(p) - (1)/(q)

If p and q are the roots of the equation x^(2)-3x+2=0 , find the value of (1)/(q)-(1)/(q) .

If 2+i sqrt(3) is a root of the equation x^(2)+p x+q=0 , where p, q are real, then (p, q)=

If P={a,b,c} and Q={r}, form the sets P xx Q and Q xx P .

If one root of the equations x^(2) + px +q=0 is 3 times the other , prove that 3p^(2) = 16q.

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 lterms of p ,q ,r ,a n dsdot Deduce the condition that the equation has a common root.