What are the solutions to the equation 2x^4-3x^3+12x^2-16x+5=0 ?

The solutions to the equation 2x^4-3x^3+12x^2-16x+5=0 are x=1,x\approx 0.45620…

Find the zeros of 2x^4-3x^3+12x^2-16x+5=0

The zeros of 2x^4-3x^3+12x^2-16x+5=0 are x=1,x\approx 0.45620…

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2 x^{4} - 3 x^{3} + 12 x^{2} - 16 x + 5 = 0

x = 1, x \approx 0.45620 \dots

Solution steps

2 x^{4} - 3 x^{3} + 12 x^{2} - 16 x + 5 = 0

Factor

2 x^{4} - 3 x^{3} + 12 x^{2} - 16 x + 5 : (x - 1) (2 x^{3} - x^{2} + 11 x - 5)

(x - 1) (2 x^{3} - x^{2} + 11 x - 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or 2 x^{3} - x^{2} + 11 x - 5 = 0

Solve

x - 1 = 0 : x = 1

Solve

2 x^{3} - x^{2} + 11 x - 5 = 0 : x \approx 0.45620 \dots

The solutions are

x = 1, x \approx 0.45620 \dots

2 x^{3} = 48

x (2 x + 3) (4 x^{2} - 81) = 0

x^{9} = 2

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

x^{4} - 12 x^{2} + 4 = 0

What are the solutions to the equation 2x^4-3x^3+12x^2-16x+5=0 ?
The solutions to the equation 2x^4-3x^3+12x^2-16x+5=0 are x=1,x\approx 0.45620…
Find the zeros of 2x^4-3x^3+12x^2-16x+5=0
The zeros of 2x^4-3x^3+12x^2-16x+5=0 are x=1,x\approx 0.45620…