What are the solutions to the equation 15X^4-445X^2+8000=0 ?

The solutions to the equation 15X^4-445X^2+8000=0 are

Find the zeros of 15X^4-445X^2+8000=0

The zeros of 15X^4-445X^2+8000=0 are

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15 X^{4} - 445 X^{2} + 8000 = 0

X = \frac{89 + 80 3}{2 3} + \frac{11279}{2 3 89 + 80 3} i, X = - \frac{89 + 80 3}{2 3} - \frac{11279}{2 3 89 + 80 3} i, X = \frac{89 + 80 3}{2 3} - \frac{11279}{2 3 89 + 80 3} i, X = - \frac{89 + 80 3}{2 3} + \frac{11279}{2 3 89 + 80 3} i

Solution steps

15 X^{4} - 445 X^{2} + 8000 = 0

Rewrite the equation with

u = X^{2}

and

u^{2} = X^{4}

15 u^{2} - 445 u + 8000 = 0

Solve

15 u^{2} - 445 u + 8000 = 0 : u = \frac{89}{6} + i \frac{11279}{6}, u = \frac{89}{6} - i \frac{11279}{6}

u = \frac{89}{6} + i \frac{11279}{6}, u = \frac{89}{6} - i \frac{11279}{6}

Substitute back

u = X^{2},

solve for

X

Solve

X^{2} = \frac{89}{6} + i \frac{11279}{6} : X = \frac{89 + 80 3}{2 3} + \frac{11279}{2 3 89 + 80 3} i, X = - \frac{89 + 80 3}{2 3} - \frac{11279}{2 3 89 + 80 3} i

Solve

X^{2} = \frac{89}{6} - i \frac{11279}{6} : X = \frac{89 + 80 3}{2 3} - \frac{11279}{2 3 89 + 80 3} i, X = - \frac{89 + 80 3}{2 3} + \frac{11279}{2 3 89 + 80 3} i

The solutions are

X = \frac{89 + 80 3}{2 3} + \frac{11279}{2 3 89 + 80 3} i, X = - \frac{89 + 80 3}{2 3} - \frac{11279}{2 3 89 + 80 3} i, X = \frac{89 + 80 3}{2 3} - \frac{11279}{2 3 89 + 80 3} i, X = - \frac{89 + 80 3}{2 3} + \frac{11279}{2 3 89 + 80 3} i

4 x - 4 x^{6} = 0

4 X + X^{4} + 9 X + 18 = 12 (X + 2)

(1 + x)^{12} = 1.1

x^{3} + 5 x^{2} - 24 x = 0

x^{3} + 3 x^{2} + 2 x + 1.06 = 0

What are the solutions to the equation 15X^4-445X^2+8000=0 ?
The solutions to the equation 15X^4-445X^2+8000=0 are
Find the zeros of 15X^4-445X^2+8000=0
The zeros of 15X^4-445X^2+8000=0 are