What are the solutions to the equation 2x^4-13x^3+28x^2=23x-6 ?

The solutions to the equation 2x^4-13x^3+28x^2=23x-6 are x=1,x=2,x= 1/2 ,x=3

Find the zeros of 2x^4-13x^3+28x^2=23x-6

The zeros of 2x^4-13x^3+28x^2=23x-6 are x=1,x=2,x= 1/2 ,x=3

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2 x^{4} - 13 x^{3} + 28 x^{2} = 23 x - 6

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

Decimal Notation

x = 1, x = 2, x = 0.5, x = 3

Solution steps

2 x^{4} - 13 x^{3} + 28 x^{2} = 23 x - 6

Move

6

to the left side

2 x^{4} - 13 x^{3} + 28 x^{2} + 6 = 23 x

Move

23 x

to the left side

2 x^{4} - 13 x^{3} + 28 x^{2} + 6 - 23 x = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

2 x^{4} - 13 x^{3} + 28 x^{2} - 23 x + 6 = 0

Factor

2 x^{4} - 13 x^{3} + 28 x^{2} - 23 x + 6 : (x - 1) (x - 2) (2 x - 1) (x - 3)

(x - 1) (x - 2) (2 x - 1) (x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

x - 2 = 0 : x = 2

Solve

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

Solve

x - 3 = 0 : x = 3

The solutions are

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

x, lo g_{10} (y) = - x^{3}

(x^{2} - 3 x + 2) (x^{2} - 9 x + 20) (x^{2} - 9 x + 18) = 720

- a^{3} + 3 a^{2} - 3 a + 1 = 0

(x - 2)^{4} = 0

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

What are the solutions to the equation 2x^4-13x^3+28x^2=23x-6 ?
The solutions to the equation 2x^4-13x^3+28x^2=23x-6 are x=1,x=2,x= 1/2 ,x=3
Find the zeros of 2x^4-13x^3+28x^2=23x-6
The zeros of 2x^4-13x^3+28x^2=23x-6 are x=1,x=2,x= 1/2 ,x=3