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

Determine all real values of the parameter 'a' for which the equation 16x^4 - ax^3 + (2a + 17) x^2 - ax + 16 = 0 has exactly four distinct real roots that form a geometric progression.

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.

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.

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.

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.

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.