x^(2)+k(2x+k-1)+2=0

Find the values of k for which roots of the following equations are real and equal: (i) 12x^(2)+4kx+3=0 (ii) kx^(2)-5x+k=0 (iii) x^(2)+k(4x+k-1)+2=0 (iv) x^(2)-2(5+2k)x+3(7+10k)=0 (v) 5x^(2)-4x+2+k(4x^(2)-2x-1)=0 (vi) (k+1)x^(2)-2(k-1)x+1=0 (vii) x^(2)-(3k-1)x+2k^(2)+2k-11=0 (viii) 2(k-12)x^(2)+2(k-12)x+2=0

Find the values of k for which the roots are real and equal in the following equations: x^(2)-2(k+1)x+k^(2)=0 (ii) k^(2)x^(2)-2(2k-1)x+4=0

If the equation x^(2)-(2k+1)x+k+2=0 has exactly one root in (0,2) such that maximum possible negative integral value of k is m and minimum possible positive integral value of k is M ,then |M - m| is

If - 1 + i is a root of x^(4) + 4x^(3) + 5x^(2) + 2x + k = 0 then k =

The number of value of k for which [x^(2)-(k-2)x+k^(2)]xx[x^(2)+kx+(2k-1)] is a perfect square is a.2.1 c.0 d.none of these

If int _(0)^(1) (3x ^(2) + 2x +k) dx =0, then find the value of k.

What is the least integral value of k for which the equation x^(2) - 2(k-1)x + (2k+1)=0 has both the roots positive ?

Let f(x)=(a_(2k)x^(2k)+a_(2k-1)x^(2k-1)+...+a_(1)x+a_(0))/(b_(2k)x^(2k)+b_(2k-1)x^(2k-1)+...+b_(1)x+b_(0)) , where k is a positive integer, a_(i), b_(i) in R " and " a_(2k) ne 0, b_(2k) ne 0 such that b_(2k)x^(2k)+b_(2k-1)x^(2k-1)+...+b_(1)x+b_(0)=0 has no real roots, then

Let f(x)=(a_(2k)x^(2k)+a_(2k-1)x^(2k-1)+...+a_(1)x+a_(0))/(b_(2k)x^(2k)+b_(2k-1)x^(2k-1)+...+b_(1)x+b_(0)) , where k is a positive integer, a_(i), b_(i) in R " and " a_(2k) ne 0, b_(2k) ne 0 such that b_(2k)x^(2k)+b_(2k-1)x^(2k-1)+...+b_(1)x+b_(0)=0 has no real roots, then