What are the solutions to the equation t^4-5t^3+5t^2+17t-42=0 ?

The solutions to the equation t^4-5t^3+5t^2+17t-42=0 are t=-2,t=3,t=2+sqrt(3)i,t=2-sqrt(3)i

Find the zeros of t^4-5t^3+5t^2+17t-42=0

The zeros of t^4-5t^3+5t^2+17t-42=0 are t=-2,t=3,t=2+sqrt(3)i,t=2-sqrt(3)i

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t^{4} - 5 t^{3} + 5 t^{2} + 17 t - 42 = 0

t = - 2, t = 3, t = 2 + 3 i, t = 2 - 3 i

Solution steps

t^{4} - 5 t^{3} + 5 t^{2} + 17 t - 42 = 0

Factor

t^{4} - 5 t^{3} + 5 t^{2} + 17 t - 42 : (t + 2) (t - 3) (t^{2} - 4 t + 7)

(t + 2) (t - 3) (t^{2} - 4 t + 7) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

t + 2 = 0 or t - 3 = 0 or t^{2} - 4 t + 7 = 0

Solve

t + 2 = 0 : t = - 2

Solve

t - 3 = 0 : t = 3

Solve

t^{2} - 4 t + 7 = 0 : t = 2 + 3 i, t = 2 - 3 i

The solutions are

t = - 2, t = 3, t = 2 + 3 i, t = 2 - 3 i

3 x^{4} - 4 x^{3} - 12 x^{2} - 4 = 0

6 x^{3} + x^{2} - 24 x - 4 = 0

x, x^{3} + y^{3} = 27

x^{3} + 6 x^{2} - 81 = 0

x, x^{3} + y^{3} = 18

What are the solutions to the equation t^4-5t^3+5t^2+17t-42=0 ?
The solutions to the equation t^4-5t^3+5t^2+17t-42=0 are t=-2,t=3,t=2+sqrt(3)i,t=2-sqrt(3)i
Find the zeros of t^4-5t^3+5t^2+17t-42=0
The zeros of t^4-5t^3+5t^2+17t-42=0 are t=-2,t=3,t=2+sqrt(3)i,t=2-sqrt(3)i