What are the solutions to the equation 12x^5=20x^4+8x^2-16 ?

The solutions to the equation 12x^5=20x^4+8x^2-16 are x=1,x\approx-0.78362…,x\approx 1.74152…

Find the zeros of 12x^5=20x^4+8x^2-16

The zeros of 12x^5=20x^4+8x^2-16 are x=1,x\approx-0.78362…,x\approx 1.74152…

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12 x^{5} = 20 x^{4} + 8 x^{2} - 16

x = 1, x \approx - 0.78362 \dots, x \approx 1.74152 \dots

Solution steps

12 x^{5} = 20 x^{4} + 8 x^{2} - 16

Move

16

to the left side

12 x^{5} + 16 = 20 x^{4} + 8 x^{2}

Move

8 x^{2}

to the left side

12 x^{5} + 16 - 8 x^{2} = 20 x^{4}

Move

20 x^{4}

to the left side

12 x^{5} + 16 - 8 x^{2} - 20 x^{4} = 0

Write in the standard form

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

12 x^{5} - 20 x^{4} - 8 x^{2} + 16 = 0

Factor

12 x^{5} - 20 x^{4} - 8 x^{2} + 16 : 4 (x - 1) (3 x^{4} - 2 x^{3} - 2 x^{2} - 4 x - 4)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

Solve

x - 1 = 0 : x = 1

Solve

3 x^{4} - 2 x^{3} - 2 x^{2} - 4 x - 4 = 0 : x \approx - 0.78362 \dots, x \approx 1.74152 \dots

The solutions are

x = 1, x \approx - 0.78362 \dots, x \approx 1.74152 \dots

5.3 \cdot 1 0^{- 9} = (y) (2 y)^{2}

x^{4} - 98715 x^{2} + 1040 = 0

3 x^{3} - 243 x = 0

x^{3} + 2 x^{2} - 21 x + 35 = 0

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

What are the solutions to the equation 12x^5=20x^4+8x^2-16 ?
The solutions to the equation 12x^5=20x^4+8x^2-16 are x=1,x\approx-0.78362…,x\approx 1.74152…
Find the zeros of 12x^5=20x^4+8x^2-16
The zeros of 12x^5=20x^4+8x^2-16 are x=1,x\approx-0.78362…,x\approx 1.74152…