If `alpha` is a complex number and `x^2+alphax+bar alpha=0` has a real root `lambda` then `lambda=`

If alpha is a complex constant such that alpha z^2+z+bar( alpha)=0 has a real root, then

If alpha is a complex constant such that alpha^(2)+z+bar(alpha)=0 has a real root then

If alpha is a complex constant such that alpha z^2+z+ baralpha=0 has a real root, then (a) alpha+ bar alpha=1 (b) alpha+ bar alpha=0 (c) alpha+ bar alpha=-1 (d)the absolute value of the real root is 1

If alpha is a complex constant such that alpha z^2+z+ baralpha=0 has a real root, then (a) alpha+ bar alpha=1 (b) alpha+ bar alpha=0 (c) alpha+ bar alpha=-1 (d)the absolute value of the real root is 1

If alpha is a complex constant such that alpha z^(2)+z+bar(alpha)=0 has a real root,then (a) alpha+bar(alpha)=1 (b) alpha+bar(alpha)=0( c) alpha+bar(alpha)=-1 (d)the absolute value of the real root is 1

If alpha,beta are roots of x^2-x+2lambda=0 and alpha,gamma are roots of 3x^2-10x+27lambda=0 then value of (betagamma)/(lambda) is

Let S be the set of all non-zero real numbers alpha such that the quadratic equation alphax^2-x+alpha=0 has two distinct real roots x_1 and x_2 satisfying the inequality abs(x_1-x_2)lt1 . Which of the following intervals is (are) a subset(s) of S ?

Let lambda and alpha be real. Find the set of all values of lambda for which the system of linear equations lambdax + ("sin"alpha)y + ("cos" alpha)z =0 , x + ("cos"alpha)y + ("sin" alpha) z =0 and -x + ("sin" alpha)y -("cos" alpha)z =0 has a non-trivial solution. For lambda =1 , find all values of alpha .