What are the solutions to the equation 2a^4-15a^2+27=0 ?

The solutions to the equation 2a^4-15a^2+27=0 are a= 3/(sqrt(2)),a=-3/(sqrt(2)),a=sqrt(3),a=-sqrt(3)

Find the zeros of 2a^4-15a^2+27=0

The zeros of 2a^4-15a^2+27=0 are a= 3/(sqrt(2)),a=-3/(sqrt(2)),a=sqrt(3),a=-sqrt(3)

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2 a^{4} - 15 a^{2} + 27 = 0

a = \frac{3}{2}, a = - \frac{3}{2}, a = 3, a = - 3

Decimal Notation

a = 2.12132 \dots, a = - 2.12132 \dots, a = 1.73205 \dots, a = - 1.73205 \dots

Solution steps

2 a^{4} - 15 a^{2} + 27 = 0

Rewrite the equation with

u = a^{2}

and

u^{2} = a^{4}

2 u^{2} - 15 u + 27 = 0

Solve

2 u^{2} - 15 u + 27 = 0 : u = \frac{9}{2}, u = 3

u = \frac{9}{2}, u = 3

Substitute back

u = a^{2},

solve for

a

Solve

a^{2} = \frac{9}{2} : a = \frac{3}{2}, a = - \frac{3}{2}

Solve

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

The solutions are

a = \frac{3}{2}, a = - \frac{3}{2}, a = 3, a = - 3

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

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

m^{3} - 6 m^{2} + 12 m + 208 = 0

(\frac{x \cdot 4 - 7}{3})^{3} = 27

4 x^{14} - 57 = 37

What are the solutions to the equation 2a^4-15a^2+27=0 ?
The solutions to the equation 2a^4-15a^2+27=0 are a= 3/(sqrt(2)),a=-3/(sqrt(2)),a=sqrt(3),a=-sqrt(3)
Find the zeros of 2a^4-15a^2+27=0
The zeros of 2a^4-15a^2+27=0 are a= 3/(sqrt(2)),a=-3/(sqrt(2)),a=sqrt(3),a=-sqrt(3)