One root of each equation below is the same fore very equati

One root of each equation below is the same fore very equation. What is the root?

a. 10x³ – 25x² – 15x = 0 (I got 3 & -1/2)

b. 6x³ – 33x² + 45x = 0 (I got 5/2 & 3)

c. 3x⁴ + 14x³ + 8x² = 0 (I got -4, -2/3)

d. 18x⁴ - 50x² = 0 (I got 5/2 & -5/2)

I have done grouping, common factor & the quadratic equation & found roots that balance the equation but I can\'t find one that is in common with them all. Am I reading the question wrong?

Solution

We can easily see that from each equation we can take out x as common

10x3 – 25x2 – 15x = 0 ----> x(10x^2 -25x -15)

b. 6x3 – 33x2 + 45x = 0 -----> x(6x^2 -33x +45)

c. 3x4 + 14x3 + 8x2 = 0 ------>x^2(3x^2 +14x +8)

d. 18x4 - 50x2 = 0 -------------> x^2(18x^2 -50)

So, x=0 is the common root for each equation