What are the solutions to the equation -15y^4=(D)(3y^2) ?

The solutions to the equation -15y^4=(D)(3y^2) are y=0,y=isqrt(D/5),y=-isqrt(D/5)

Find the zeros of -15y^4=(D)(3y^2)

The zeros of -15y^4=(D)(3y^2) are y=0,y=isqrt(D/5),y=-isqrt(D/5)

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- 15 y^{4} = (D) (3 y^{2})

y = 0, y = i \frac{D}{5}, y = - i \frac{D}{5}

Solution steps

- 15 y^{4} = (D) (3 y^{2})

Move

(D) (3 y^{2})

to the left side

- 15 y^{4} - D \cdot 3 y^{2} = 0

Factor

- 15 y^{4} - D \cdot 3 y^{2} : - 3 y^{2} (5 y^{2} + D)

- 3 y^{2} (5 y^{2} + D) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y = 0 or 5 y^{2} + D = 0

Solve

5 y^{2} + D = 0 : y = i \frac{D}{5}, y = - i \frac{D}{5}

The solutions are

y = 0, y = i \frac{D}{5}, y = - i \frac{D}{5}

x^{6} + x^{3} - 42 = 0

6 y^{2} + 9 y = 15 y^{3}

x^{3} + 3 x^{2} - 4 x + 12 = 0

5 x^{3} + 30 x^{2} + 45 = 0

12 x^{3} + 24 x^{2} = 0

What are the solutions to the equation -15y^4=(D)(3y^2) ?
The solutions to the equation -15y^4=(D)(3y^2) are y=0,y=isqrt(D/5),y=-isqrt(D/5)
Find the zeros of -15y^4=(D)(3y^2)
The zeros of -15y^4=(D)(3y^2) are y=0,y=isqrt(D/5),y=-isqrt(D/5)