What are the solutions to the equation roots 2x^3-11x^2+12x+9 ?

The solutions to the equation roots 2x^3-11x^2+12x+9 are x=3,x=-1/2

Find the zeros of roots 2x^3-11x^2+12x+9

The zeros of roots 2x^3-11x^2+12x+9 are x=3,x=-1/2

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roots

2 x^{3} - 11 x^{2} + 12 x + 9

x = 3, x = - \frac{1}{2}

Solution steps

2 x^{3} - 11 x^{2} + 12 x + 9

The roots are the intercepts with the x-axis

(y = 0)

2 x^{3} - 11 x^{2} + 12 x + 9 = 0

Factor

2 x^{3} - 11 x^{2} + 12 x + 9 : (x - 3)^{2} (2 x + 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or 2 x + 1 = 0

Solve

x - 3 = 0 : x = 3

Solve

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

The solutions are

x = 3, x = - \frac{1}{2}

2 x^{4} - x^{3} - 7 x^{2} + x + 2 = 0

x^{4} - 5 x^{2} - 36 = 0

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

6 x + 12 = 3 x^{3}

- 5 x^{5} + 5 x = 0

What are the solutions to the equation roots 2x^3-11x^2+12x+9 ?
The solutions to the equation roots 2x^3-11x^2+12x+9 are x=3,x=-1/2
Find the zeros of roots 2x^3-11x^2+12x+9
The zeros of roots 2x^3-11x^2+12x+9 are x=3,x=-1/2