What are the solutions to the equation 2t^3-3t^2-2t-42=0 ?

The solutions to the equation 2t^3-3t^2-2t-42=0 are t= 7/2 ,t=-1+sqrt(5)i,t=-1-sqrt(5)i

Find the zeros of 2t^3-3t^2-2t-42=0

The zeros of 2t^3-3t^2-2t-42=0 are t= 7/2 ,t=-1+sqrt(5)i,t=-1-sqrt(5)i

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2 t^{3} - 3 t^{2} - 2 t - 42 = 0

t = \frac{7}{2}, t = - 1 + 5 i, t = - 1 - 5 i

Solution steps

2 t^{3} - 3 t^{2} - 2 t - 42 = 0

Factor

2 t^{3} - 3 t^{2} - 2 t - 42 : (2 t - 7) (t^{2} + 2 t + 6)

(2 t - 7) (t^{2} + 2 t + 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

2 t - 7 = 0 or t^{2} + 2 t + 6 = 0

Solve

2 t - 7 = 0 : t = \frac{7}{2}

Solve

t^{2} + 2 t + 6 = 0 : t = - 1 + 5 i, t = - 1 - 5 i

The solutions are

t = \frac{7}{2}, t = - 1 + 5 i, t = - 1 - 5 i

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

- x^{3} + 10 x^{2} - 33 x + 36 = 0

3 x^{3} - 24 x^{2} + 21 x = 0

x^{3} - 6 x = 3 x^{2} - 8

y^{4} - 4 y = 0

What are the solutions to the equation 2t^3-3t^2-2t-42=0 ?
The solutions to the equation 2t^3-3t^2-2t-42=0 are t= 7/2 ,t=-1+sqrt(5)i,t=-1-sqrt(5)i
Find the zeros of 2t^3-3t^2-2t-42=0
The zeros of 2t^3-3t^2-2t-42=0 are t= 7/2 ,t=-1+sqrt(5)i,t=-1-sqrt(5)i