What are the solutions to the equation 3x^4-7x-3x^2+5x+2=0 ?

The solutions to the equation 3x^4-7x-3x^2+5x+2=0 are x=1,x\approx 0.63797…

Find the zeros of 3x^4-7x-3x^2+5x+2=0

The zeros of 3x^4-7x-3x^2+5x+2=0 are x=1,x\approx 0.63797…

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3 x^{4} - 7 x - 3 x^{2} + 5 x + 2 = 0

x = 1, x \approx 0.63797 \dots

Solution steps

3 x^{4} - 7 x - 3 x^{2} + 5 x + 2 = 0

Refine

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

3 x^{3} + 3 x^{2} - 2 = 0 : x \approx 0.63797 \dots

The solutions are

x = 1, x \approx 0.63797 \dots

x^{4} - 2 x^{3} - 6 x^{2} = 0

1.576 = (1 + x)^{3}

420 = 130 x^{3} + 30

0 = - x^{3} + 4 \cdot x

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

What are the solutions to the equation 3x^4-7x-3x^2+5x+2=0 ?
The solutions to the equation 3x^4-7x-3x^2+5x+2=0 are x=1,x\approx 0.63797…
Find the zeros of 3x^4-7x-3x^2+5x+2=0
The zeros of 3x^4-7x-3x^2+5x+2=0 are x=1,x\approx 0.63797…