What are the solutions to the equation ax+bx^3=0 ?

The solutions to the equation ax+bx^3=0 are x=0,x=isqrt(a/b),x=-isqrt(a/b);\quad b\ne 0

Find the zeros of ax+bx^3=0

The zeros of ax+bx^3=0 are x=0,x=isqrt(a/b),x=-isqrt(a/b);\quad b\ne 0

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a x + b x^{3} = 0

x = 0, x = i \frac{a}{b}, x = - i \frac{a}{b}; b \neq = 0

Solution steps

a x + b x^{3} = 0

Factor

a x + b x^{3} : x (a + b x^{2})

x (a + b x^{2}) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or a + b x^{2} = 0

Solve

a + b x^{2} = 0 : x = i \frac{a}{b}, x = - i \frac{a}{b}; b \neq = 0

The solutions are

x = 0, x = i \frac{a}{b}, x = - i \frac{a}{b}; b \neq = 0

1 - x^{2} = 24 x^{3}

x^{3} + 2 x^{2} - 10 x - 19 = 0

a^{3} = 5 (3) - 1

(3 x - 1)^{2} = (3 x - 1)^{3}

50 \cdot x^{30} = 1000

What are the solutions to the equation ax+bx^3=0 ?
The solutions to the equation ax+bx^3=0 are x=0,x=isqrt(a/b),x=-isqrt(a/b);\quad b\ne 0
Find the zeros of ax+bx^3=0
The zeros of ax+bx^3=0 are x=0,x=isqrt(a/b),x=-isqrt(a/b);\quad b\ne 0