`If p^(2) x^(2) - q^(2) = 0 , then x is `

If x^(2) - 3x + 2 is factor of x^(4) - px^(2) + q then 2q - p is equal to

If p and q are roots of the quadratic equation x^(2) + mx + m^(2) + a = 0 , then the value of p^(2) + q^(2) + pq , is

Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,2beta be the roots of the equation x^(2)-qx+r=0 , then the value of r is (1) (2)/(9)(p-q)(2q-p) (2) (2)/(9)(q-p)(2p-q) (3) (2)/(9)(q-2p)(2q-p) (4) (2)/(9)(2p-q)(2q-p)

If the circles x^(2) + y^(2) + 5 Kx + 2y + K = 0 and 2x^(2) + y^(2)) + 2Kx + 3y - 1 = 0, (K in R) intersect at the point P and Q then the line 4x + 5y - K = 0 passes P and Q for :

If 2 + isqrt3 is a root of x^(3) - 6x^(2) + px + q = 0 (where p and q are real) then p + q is

If a, b are the roots of equation x^(2)-3x + p =0 and c, d are the roots of x^(2) - 12x + q = 0 and a, b, c, d are in G.P., then prove that : p : q =1 : 16

Let f(x)=x^(2)+2px+2q^(2) and g(x)=-x^(2)-2qx+q^(2) (where q ne0 ). If x in R and the minimum value of f(x) is equal to the maximum value of g(x) , then the value of (p^(2))/(q^(2)) is equal to

If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

If the line of regression of Y on X is p_(1)x + q_(1)y + r_(1)= 0 and that of X on Y is p_(2)x + q_(2)y + r_(2)= 0 , prove that (p_(1)q_(2))/(p_(2)q_(1)) le 1

If p (x) = x ^(2) -4x+8 and q 9x)=x-3, what is the value of (q (p (5)))/(p (q (5))) ?