Question

Using factorization method solve the quadratic equation:

3x^3 -72x^2 +24x

Answer 1

To solve the quadratic equation using factorization method, we need to first factorize the equation and then solve for x.

Given equation: 3x^3 - 72x^2 + 24x

First, let's factor out the common term (3x):
3x(x^2 - 24x + 8)

Next, we need to factorize the quadratic expression inside the parentheses.

For the quadratic expression, let's find its factors:

The quadratic expression can be written as: x^2 - 24x + 8

We need to find two numbers whose product is 8 and whose sum is -24.
The numbers are -2 and -6, since (-2) * (-6) = 8 and (-2) + (-6) = -8.

Now, rewrite the quadratic expression using these two numbers:
x^2 - 2x - 6x + 8

Then, factor by grouping:
x(x - 2) - 4(x - 2)

Now, the quadratic expression can be written as:
(x - 2)(x - 4)

Substituting this back into the original equation, we have:
3x(x - 2)(x - 4)

Setting each factor equal to zero and solving for x:

3x = 0 --> x = 0
x - 2 = 0 --> x = 2
x - 4 = 0 --> x = 4

Therefore, the solutions to the quadratic equation are x = 0, x = 2, and x = 4.