(4-k)x^(2)+(2k+4)x+(8k+1)=0

For what value of k,(4-k)x^(2)+2(k+2)x+(8K+1) is a perfect square.

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

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

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

The largest real value for x such that sum_(k=0)^(4)((5^(4-k))/((4-k)!))((x^(k))/(k!))=(8)/(3)is

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

If the line x + 2y = k is normal to the parabola x^(2) – 4x – 8y + 12 = 0 then the value of k/4 is :