Answer:
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
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]3x^3-48x^2=0\qquad\text{divide both sides by 3}\\\\\dfrac{3x^3}{3}-\dfrac{48x^2}{3}=\dfrac{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[/tex]
