If `az^2+bz+1=0`, where `a,b in C`, `|a|=1/2` and have a root `alpha` such that `|alpha|=1` then `|abarb-b|=`

If az^(2)+bz+1=0 where a,b, in C and |a|=(1)/(2) have a root alpha such that |alpha|=1 then 4|avecb-b| is equal to

If az^(2)+bz+1=0 where a,b, in C and |a|=(1)/(2) have a root alpha such that |alpha|=1 then 4|avecb-b| is equal to

Show that the equation az^(3)+bz^(2)+bar(b)z+bar(a)=0 has a root alpha such that | alpha|=1,a,b,zand alpha belong to the set of complex numbers.

Consider the quadratic equation az^(2)+bz+c=0 where a,b,c are non-zero complex numbers. Now answer the following. The condition that the equation has one complex root alpha such that |alpha|=1 , is

Consider the quadratic equation az^(2)+bz+c=0 where a,b,c and non-zero complex numbers. Now answer the following: Q. The condition that the equation has one complex root alpha such that |alpha|=1 , is

If the roots of a_1x^2 + b_1x+ c_1 = 0 are alpha_1 ,beta_ 1 and those of a_2x^2+b_2x+c_2=0 are alpha_2,beta_2 such that alpha_1alpha_2=beta_1beta_2=1 then

Let a ,b ,c be real. If a x^2+b x+c=0 has two real roots alpha and beta ,where alpha 1 , then show that 1+c/a+|b/a|<0

Consider a quadratic equation az^(2)bz+c=0, where a,b and c are complex numbers. The condition that the equation has one purely imaginary root , is

If the roots of a_1x^(2)+b_1x+c_1=0 and alpha_1 , beta_1 and those of a_2x^(2)+b_2x+c_2=0 are alpha_2 , beta_2 such that alpha_1alpha_2=beta_1beta_2=1 then :

If the roots of a_1x^(2)+b_1x+c_1=0 and alpha_1 , beta_1 and those of a_2x^(2)+b_2x+c_2=0 are alpha_2 , beta_2 such that alpha_1alpha_2=beta_1beta_2=1 then :