What are the solutions to the equation t^3-13t^2+65t-105=0 ?

The solutions to the equation t^3-13t^2+65t-105=0 are t=3,t=5+sqrt(10)i,t=5-sqrt(10)i

Find the zeros of t^3-13t^2+65t-105=0

The zeros of t^3-13t^2+65t-105=0 are t=3,t=5+sqrt(10)i,t=5-sqrt(10)i

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t^{3} - 13 t^{2} + 65 t - 105 = 0

t = 3, t = 5 + 10 i, t = 5 - 10 i

Solution steps

t^{3} - 13 t^{2} + 65 t - 105 = 0

Factor

t^{3} - 13 t^{2} + 65 t - 105 : (t - 3) (t^{2} - 10 t + 35)

(t - 3) (t^{2} - 10 t + 35) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

t - 3 = 0 or t^{2} - 10 t + 35 = 0

Solve

t - 3 = 0 : t = 3

Solve

t^{2} - 10 t + 35 = 0 : t = 5 + 10 i, t = 5 - 10 i

The solutions are

t = 3, t = 5 + 10 i, t = 5 - 10 i

2 x^{3} - 3 x^{2} + 32 x + 17 = 0

x^{2} (x - 8) = 0

b^{3} = b

- x^{3} + x^{2} - x + 1 = 0

x (x^{3} - 1) = 0

What are the solutions to the equation t^3-13t^2+65t-105=0 ?
The solutions to the equation t^3-13t^2+65t-105=0 are t=3,t=5+sqrt(10)i,t=5-sqrt(10)i
Find the zeros of t^3-13t^2+65t-105=0
The zeros of t^3-13t^2+65t-105=0 are t=3,t=5+sqrt(10)i,t=5-sqrt(10)i