Fill in the blanks If `2+isqrt(3)` is a root of the equation `x^2+p x+q=0,w h e r epa n dq` are real, then `(p ,q)=(______,_____)` .

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

Fill in the blanks If the product of the roots of the equation x^2-3k x+2e^(21 nk)-1=0 is 7, then the roots are real for____________.

The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are

If one root is square of the other root of the equation x^2+p x+q=0 then the relation between p and q is

If the roots of the equation, x^3 + px^2+qx-1 = 0 form an increasing G.P. where p and q are real,then

If the sum of square of roots of the equation x^2+(p+i q)x+3i=0 is 8, then find the value of pa n dq j ,w h e r epa n dq are real.

Find the condition that the roots of cubic equation x^3+ax^2+bx+c=0 are in the ratio p : q : r .

If p is real, discuss the nature of the roots of the equation 4x^2+4px+p+2=0 , in terms of p.