What are the solutions to the equation x^3-16x^2+75x-90=0 ?

The solutions to the equation x^3-16x^2+75x-90=0 are x=6,x=5+sqrt(10),x=5-sqrt(10)

Find the zeros of x^3-16x^2+75x-90=0

The zeros of x^3-16x^2+75x-90=0 are x=6,x=5+sqrt(10),x=5-sqrt(10)

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x^{3} - 16 x^{2} + 75 x - 90 = 0

x = 6, x = 5 + 10, x = 5 - 10

Decimal Notation

x = 6, x = 8.16227 \dots, x = 1.83772 \dots

Solution steps

x^{3} - 16 x^{2} + 75 x - 90 = 0

Factor

x^{3} - 16 x^{2} + 75 x - 90 : (x - 6) (x^{2} - 10 x + 15)

(x - 6) (x^{2} - 10 x + 15) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 6 = 0 or x^{2} - 10 x + 15 = 0

Solve

x - 6 = 0 : x = 6

Solve

x^{2} - 10 x + 15 = 0 : x = 5 + 10, x = 5 - 10

The solutions are

x = 6, x = 5 + 10, x = 5 - 10

x, \frac{d ^{2} x}{d t ^{2}} = 2 x^{3}

x^{4} + 11 x^{2} = 0

x^{3} - x = 0

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

x^{3} - 13 x^{2} - x + 13 = 0

What are the solutions to the equation x^3-16x^2+75x-90=0 ?
The solutions to the equation x^3-16x^2+75x-90=0 are x=6,x=5+sqrt(10),x=5-sqrt(10)
Find the zeros of x^3-16x^2+75x-90=0
The zeros of x^3-16x^2+75x-90=0 are x=6,x=5+sqrt(10),x=5-sqrt(10)