What are the solutions to the equation 3x^4+5x^3-11x^2+2x-3=0 ?

The solutions to the equation 3x^4+5x^3-11x^2+2x-3=0 are x=-3,x\approx 1.27674…

Find the zeros of 3x^4+5x^3-11x^2+2x-3=0

The zeros of 3x^4+5x^3-11x^2+2x-3=0 are x=-3,x\approx 1.27674…

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3 x^{4} + 5 x^{3} - 11 x^{2} + 2 x - 3 = 0

x = - 3, x \approx 1.27674 \dots

Solution steps

3 x^{4} + 5 x^{3} - 11 x^{2} + 2 x - 3 = 0

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x + 3 = 0 : x = - 3

Solve

3 x^{3} - 4 x^{2} + x - 1 = 0 : x \approx 1.27674 \dots

The solutions are

x = - 3, x \approx 1.27674 \dots

x^{2} (x^{2} - 81) - 49 (x^{2} - 81) = 0

3 x^{3} - 5 x^{2} - 1 = 0

(x + 2)^{4} = 81

5 = 4 x^{3} + 12 x^{2} + 12 x + 4

(m - 1)^{2} (m^{2} + 1)^{2} = 0

What are the solutions to the equation 3x^4+5x^3-11x^2+2x-3=0 ?
The solutions to the equation 3x^4+5x^3-11x^2+2x-3=0 are x=-3,x\approx 1.27674…
Find the zeros of 3x^4+5x^3-11x^2+2x-3=0
The zeros of 3x^4+5x^3-11x^2+2x-3=0 are x=-3,x\approx 1.27674…