What are the solutions to the equation 2x^3-21x^2+71x-78=0 ?

The solutions to the equation 2x^3-21x^2+71x-78=0 are x=3,x=(15+sqrt(17))/4 ,x=(15-sqrt(17))/4

Find the zeros of 2x^3-21x^2+71x-78=0

The zeros of 2x^3-21x^2+71x-78=0 are x=3,x=(15+sqrt(17))/4 ,x=(15-sqrt(17))/4

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2 x^{3} - 21 x^{2} + 71 x - 78 = 0

x = 3, x = \frac{15 + 17}{4}, x = \frac{15 - 17}{4}

Decimal Notation

x = 3, x = 4.78077 \dots, x = 2.71922 \dots

Solution steps

2 x^{3} - 21 x^{2} + 71 x - 78 = 0

Factor

2 x^{3} - 21 x^{2} + 71 x - 78 : (x - 3) (2 x^{2} - 15 x + 26)

(x - 3) (2 x^{2} - 15 x + 26) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or 2 x^{2} - 15 x + 26 = 0

Solve

x - 3 = 0 : x = 3

Solve

2 x^{2} - 15 x + 26 = 0 : x = \frac{15 + 17}{4}, x = \frac{15 - 17}{4}

The solutions are

x = 3, x = \frac{15 + 17}{4}, x = \frac{15 - 17}{4}

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

3 x^{3} - 25 x^{2} + 58 x - 40

6 x^{3} = 0

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

- 39 = 1 - 5 x^{9}

What are the solutions to the equation 2x^3-21x^2+71x-78=0 ?
The solutions to the equation 2x^3-21x^2+71x-78=0 are x=3,x=(15+sqrt(17))/4 ,x=(15-sqrt(17))/4
Find the zeros of 2x^3-21x^2+71x-78=0
The zeros of 2x^3-21x^2+71x-78=0 are x=3,x=(15+sqrt(17))/4 ,x=(15-sqrt(17))/4