Question

What are the roots of the equation?

5x³ + 45x² + 70x = 0

A. {−7, −2, 0}
B. {−7, 0, 2}
C. {0, 2, 7}
D. {−2, 0, 7}

Answer 1

The roots of the equation 5x³ + 45x² + 70x = 0 are -7, -2, and 0.

Step-by-step explanation:

To find the roots of the equation 5x³ + 45x² + 70x = 0, we can factor out an x from each term, giving us x(5x² + 45x + 70) = 0. Then, we can solve each factor separately.

Setting x = 0, we get one root of x = 0. To solve the quadratic factor 5x² + 45x + 70 = 0, we can use the quadratic formula. The roots of this quadratic equation are x = -7 and x = -2.

Therefore, the roots of the original equation are x = -7, x = -2, and x = 0. So, the correct answer is Option B. {-7, 0, 2}.