What are the solutions to the equation 120t^2-15t^4=0 ?

The solutions to the equation 120t^2-15t^4=0 are t=0,t=2sqrt(2),t=-2sqrt(2)

Find the zeros of 120t^2-15t^4=0

The zeros of 120t^2-15t^4=0 are t=0,t=2sqrt(2),t=-2sqrt(2)

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120 t^{2} - 15 t^{4} = 0

t = 0, t = 22, t = - 22

Decimal

t = 0, t = 2.82842 \dots, t = - 2.82842 \dots

Solution steps

120 t^{2} - 15 t^{4} = 0

Write in the standard form

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

- 15 t^{4} + 120 t^{2} = 0

Rewrite the equation with

u = t^{2}

and

u^{2} = t^{4}

- 15 u^{2} + 120 u = 0

Solve

- 15 u^{2} + 120 u = 0 : u = 0, u = 8

u = 0, u = 8

Substitute back

u = t^{2},

solve for

t

Solve

t^{2} = 0 : t = 0

Solve

t^{2} = 8 : t = 22, t = - 22

The solutions are

t = 0, t = 22, t = - 22

x^{5} - x^{4} - 10 x^{3} + 10 x^{2} - 11 x + 11 = 0

4096 = x^{3}

12 \cdot 20 = x^{5}

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

26 = 16 \cdot (1 + x)^{4}

What are the solutions to the equation 120t^2-15t^4=0 ?
The solutions to the equation 120t^2-15t^4=0 are t=0,t=2sqrt(2),t=-2sqrt(2)
Find the zeros of 120t^2-15t^4=0
The zeros of 120t^2-15t^4=0 are t=0,t=2sqrt(2),t=-2sqrt(2)