If one root of `z^2 + (a + i)z+ b +ic =0` is real, where `a, b, c in R` , then `c^2 + b-ac=`

The roots of (x+a)(x+b)-8k=(k-2)^(2) are real and equal where a,b,c in R then

If 1/(2-sqrt(-2)) is one of the roots of ax^(2)+bx+c = 0 , where a,b, c are real, then what are the values of a,b,c respectively ?

If z_1, z_2 are the roots of the equation az^2 + bz + c = 0 , with a, b, c > 0, 2b^2 > 4ac gt b^2, z_1 in third quadrant , z_2 in second quadrant in the argand’s plane then, show that arg ((z_1)/z_2)=2cos^(-1)((b^2)/(4ac))^(1//2)

Consider the equation az + b bar(z) + c =0 , where a,b,c in Z If |a| ne |b| , then z represents

If (1 + 2i) is a root of the equation x^(2) + bx + c = 0 . Where b and c are real, then (b,c) is given by :

If a x^2+(b-c)x+a-b-c=0 has unequal real roots for all c in R ,then

If a x^2+(b-c)x+a-b-c=0 has unequal real roots for all c in R , then

If a x^2+(b-c)x+a-b-c=0 has unequal real roots for all c in R ,then

If one root of ax^(2)+bx-2c=0(a,b,c real) is imaginary and 8a+2b>c, then