What are the solutions to the equation 2x^4-21x^2+45=0 ?

The solutions to the equation 2x^4-21x^2+45=0 are x=sqrt(15/2),x=-sqrt(15/2),x=sqrt(3),x=-sqrt(3)

Find the zeros of 2x^4-21x^2+45=0

The zeros of 2x^4-21x^2+45=0 are x=sqrt(15/2),x=-sqrt(15/2),x=sqrt(3),x=-sqrt(3)

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2 x^{4} - 21 x^{2} + 45 = 0

x = \frac{15}{2}, x = - \frac{15}{2}, x = 3, x = - 3

Decimal Notation

x = 2.73861 \dots, x = - 2.73861 \dots, x = 1.73205 \dots, x = - 1.73205 \dots

Solution steps

2 x^{4} - 21 x^{2} + 45 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

2 u^{2} - 21 u + 45 = 0

Solve

2 u^{2} - 21 u + 45 = 0 : u = \frac{15}{2}, u = 3

u = \frac{15}{2}, u = 3

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = \frac{15}{2} : x = \frac{15}{2}, x = - \frac{15}{2}

Solve

x^{2} = 3 : x = 3, x = - 3

The solutions are

x = \frac{15}{2}, x = - \frac{15}{2}, x = 3, x = - 3

2 x^{3} = x^{2}

4 x^{3} + x^{2} - 36 x - 9 = 0

(x + 2) (x - 1) (x - 3) = - 3

m^{3} = 2

- x^{3} + x^{2} + 14 x + 11 = 0

What are the solutions to the equation 2x^4-21x^2+45=0 ?
The solutions to the equation 2x^4-21x^2+45=0 are x=sqrt(15/2),x=-sqrt(15/2),x=sqrt(3),x=-sqrt(3)
Find the zeros of 2x^4-21x^2+45=0
The zeros of 2x^4-21x^2+45=0 are x=sqrt(15/2),x=-sqrt(15/2),x=sqrt(3),x=-sqrt(3)