For what values of the parameter `a` the equation `x^(4)+2ax^(3)+x^(2)+2ax+1=0` has atleast two distinct negative roots?

Find all values of the parameter a for which the quadratic equation (a+1)x^(2)+2(a+1)x+a-2=0 (i) has two distinct roots. (ii) has no roots. (iii) has to equal roots.

The values of the parameter a for which the quadratic equations (12a)x^(2)6 ax11=0 and ax^(2)x+1=0 have at least one root in common are

The value of a for which the equation (1-a^(2))x^(2)+2ax-1=0 has roots belonging to (0,1) is

If the equation x^(3)-3ax^(2)+3bx-c=0 has positive and distinct roots, then

if the equation x^(4)-4x^(3)+ax^(2)+bx+1=0 has four positive roots, then find a.

Suppose a, b, c are real numbers, and each of the equations x^(2)+2ax+b^(2)=0 and x^(2)+2bx+c^(2)=0 has two distinct real roots. Then the equation x^(2)+2cx+a^(2)=0 has - (A) Two distinct positive real roots (B) Two equal roots (C) One positive and one negative root (D) No real roots