What are the solutions to the equation 2x^4+5x^3+4=x^2 ?

The solutions to the equation 2x^4+5x^3+4=x^2 are x=-1,x\approx-2.57716…

Find the zeros of 2x^4+5x^3+4=x^2

The zeros of 2x^4+5x^3+4=x^2 are x=-1,x\approx-2.57716…

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2 x^{4} + 5 x^{3} + 4 = x^{2}

x = - 1, x \approx - 2.57716 \dots

Solution steps

2 x^{4} + 5 x^{3} + 4 = x^{2}

Move

x^{2}

to the left side

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

Write in the standard form

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

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

Factor

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

(x + 1) (2 x^{3} + 3 x^{2} - 4 x + 4) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or 2 x^{3} + 3 x^{2} - 4 x + 4 = 0

Solve

x + 1 = 0 : x = - 1

Solve

2 x^{3} + 3 x^{2} - 4 x + 4 = 0 : x \approx - 2.57716 \dots

The solutions are

x = - 1, x \approx - 2.57716 \dots

x^{4} - 34 x^{2} + 225 = 0

x^{4} - 7 x^{2} + 6 = 0

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

x^{3} = 30 3^{3} + 40 4^{3} + 50 5^{3}

x^{4} - 8 x^{2} + 7 = 0

What are the solutions to the equation 2x^4+5x^3+4=x^2 ?
The solutions to the equation 2x^4+5x^3+4=x^2 are x=-1,x\approx-2.57716…
Find the zeros of 2x^4+5x^3+4=x^2
The zeros of 2x^4+5x^3+4=x^2 are x=-1,x\approx-2.57716…