Question

Solve completely
3x^3-48x^2=0

Answer 1

Two solutions were found :

x = 16

x = 0

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(3 • (x3)) - (24•3x2) = 0

Step 2 :

Equation at the end of step 2 :

3x3 - (24•3x2) = 0

Step 3 :

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

3x3 - 48x2 = 3x2 • (x - 16)

Equation at the end of step 4 :

3x2 • (x - 16) = 0

Step 5 :

Theory - Roots of a product :

5.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

5.2 Solve : 3x2 = 0

Divide both sides of the equation by 3:

x2 = 0

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:

x = ± √ 0

Any root of zero is zero. This equation has one solution which is x = 0

Solving a Single Variable Equation :

5.3 Solve : x-16 = 0

Add 16 to both sides of the equation :

x = 16

Two solutions were found :

x = 16

x = 0

Explanation:

Answer 2

x = 0 or x = 16

Explanation:

`3x^3-48x^2=0\qquad\text{divide both sides by 3}\\\\(3x^3)/(3)-(48x^2)/(3)=(0)/(3)\\\\x^3-16x^2=0\qquad\text{distribute}\\\\x^2(x-16)=0\\\\\text{The product is equal to 0 when one of the factors is equal to 0.}\\\text{Therefore}\\\\x^2(x-16)=0\iff x^2=0\ \vee\ x-16=0\\\\x^2=0\Rightarrow x=0\\\\x-16=0\Rightarrow x=16`