Solve the equation t^4+10t-11=0

Thiskind of equation is called biquadratic
equation.

This equation is reduced to a quadratic equation
when doing the substitution t^2 = x.

We'll re-write the
equation in x:

x^2 +10x - 11 =
0

We'll apply quadratic
formula:

x1 = [-10+
sqrt(100+44)]/2

x1 =
(-10+12)/2

x1 = 1

x2 =
(-10-12)/2

x2 = -11

But, we'll
have to find t1,t2,t3,t4.

t^2 =
x1

t^2 = 1

t1 = sqrt 1 and t2
= -sqrt 1

t1=1 and t2=-1

t^2 =
x2

t^2 = -11

z3 = i*sqrt11 and
z4 = -i*sqrt11

The solutions of the
biquadratic equation are real and complex: { -1 ; 1 } ; {-i*sqrt11 ;
i*sqrt11}.