What are the solutions to the equation x^3+5x^2-29x+15=0 ?

The solutions to the equation x^3+5x^2-29x+15=0 are x=3,x=-4+sqrt(21),x=-4-sqrt(21)

Find the zeros of x^3+5x^2-29x+15=0

The zeros of x^3+5x^2-29x+15=0 are x=3,x=-4+sqrt(21),x=-4-sqrt(21)

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x^{3} + 5 x^{2} - 29 x + 15 = 0

x = 3, x = - 4 + 21, x = - 4 - 21

Decimal Notation

x = 3, x = 0.58257 \dots, x = - 8.58257 \dots

Solution steps

x^{3} + 5 x^{2} - 29 x + 15 = 0

Factor

x^{3} + 5 x^{2} - 29 x + 15 : (x - 3) (x^{2} + 8 x - 5)

(x - 3) (x^{2} + 8 x - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} + 8 x - 5 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{2} + 8 x - 5 = 0 : x = - 4 + 21, x = - 4 - 21

The solutions are

x = 3, x = - 4 + 21, x = - 4 - 21

(x^{2} + 3)^{2} + 21 = 10 x^{2} + 30

x^{3} + x^{2} - 9 x - 9 = 0

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

x^{3} + a x^{2} - 4 x - 4 a = 0

3 x^{5} = 24 x

What are the solutions to the equation x^3+5x^2-29x+15=0 ?
The solutions to the equation x^3+5x^2-29x+15=0 are x=3,x=-4+sqrt(21),x=-4-sqrt(21)
Find the zeros of x^3+5x^2-29x+15=0
The zeros of x^3+5x^2-29x+15=0 are x=3,x=-4+sqrt(21),x=-4-sqrt(21)