If `sqrt5-isqrt7` is a root of `ax^4+bx^3+cx^2+dx+e=0,` where a, b, c, d, e are rational numbers, then the other roots are

If 2−i is one root of the equation ax^2+bx+c=0, and a,b,c are rational numbers, then the other root is ........

If 2 + i and sqrt5-2i are the roots of the equation (x^2+ax+b)(x^2+cx+d)=0 , where a,b,c,d are real constants, then product of all roots of the equation is

The sum of the roots of the equation, ax^(2) + bx + c = 0 where a,b and c are rational and whose one of the roots is 4 - sqrt(5) is

If alpha and beta are equal rational numbers, roots of ax^(2)+bx+c=0 (where a,b,c be rational numbers ) then Delta=

If 2 + i and sqrt(5)-2i are the roots of the equation (x^(2)+ax+b)(x^(2)+cx+d)=0 where a , b , c , d are real constants then product of all roots of the equation is -

A root of equation ax^2+ bx+c=0 (where a, b and c are rational numbers) is 5 +3 sqrt3 . What is the value of (a^2 + b^2 + c^2)//(a+ b + c) ?

If x^(2)-1 is a factor of ax^(4)+bx^(3)+cx^(2)+dx+e, show that a+c+e=b+d

If (x^2-1) is a factor of ax^4+bx^3+cx^2+dx+e if that a+c+e=b+d=0