Show that `x^5 - 5x ^3 + 5x ^2 -1=0` has three equal roots and find this root.

If -1 +i is a root of x^4 + 4x^3 + 5x^2 + k=0 then its real roots are

If the equation x^(5)-10a^(3)x^(2)+b^(4)x+c^(5)=0 has three equal roots, then

The equation 3x^(2)-12x+(n-5)=0 has equal roots. Find the value of n.

Let a in R and f : R rarr R be given by f(x)=x^(5)-5x+a , then (a) f(x)=0 has three real roots if a gt 4 (b) f(x)=0 has only one real root if a gt 4 (c) f(x)=0 has three real roots if a lt -4 (d) f(x)=0 has three real roots if -4 lt a lt 4

Solve the equation x^4 -5x^3 +4x^2 +8x -8=0 given that 1- sqrt(5) is a root

Show that the equation x^(2)+5x-6=0 has real roots.

The equation x^(2)+2(m-1)x+(m+5)=0 has real and equal roots. Find the value of m.

Solve the equation x^4 +2x^3 -5x^2 +6x +2=0 given that 1+i is a root

If the equation (a - 5) x^(2) + 2 (a - 10) x + a + 10 = 0 has roots of opposite sign , then find the values of a .

The equation 3x^(2)-12x+(n-5)=0 has repeated roots. Find the value of of n.