What are the solutions to the equation x^3-7x^2+5x+6=0 ?

The solutions to the equation x^3-7x^2+5x+6=0 are x=6,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

Find the zeros of x^3-7x^2+5x+6=0

The zeros of x^3-7x^2+5x+6=0 are x=6,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

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x^{3} - 7 x^{2} + 5 x + 6 = 0

x = 6, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

Decimal Notation

x = 6, x = 1.61803 \dots, x = - 0.61803 \dots

Solution steps

x^{3} - 7 x^{2} + 5 x + 6 = 0

Factor

x^{3} - 7 x^{2} + 5 x + 6 : (x - 6) (x^{2} - x - 1)

(x - 6) (x^{2} - x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 6 = 0 or x^{2} - x - 1 = 0

Solve

x - 6 = 0 : x = 6

Solve

x^{2} - x - 1 = 0 : x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

The solutions are

x = 6, x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

3 y^{4} - 5 y^{3} + 2 y^{2} = 0

x^{3} - 5 x^{2} - 7 x + 35 = 0

x^{5} + x^{2} = 1

x^{3} = x^{7}

m^{3} = \frac{1}{125}

What are the solutions to the equation x^3-7x^2+5x+6=0 ?
The solutions to the equation x^3-7x^2+5x+6=0 are x=6,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2
Find the zeros of x^3-7x^2+5x+6=0
The zeros of x^3-7x^2+5x+6=0 are x=6,x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2