Question
Question: How do you solve \[15{{x}^{3}}-65{{x}^{2}}-150x=0\]?...
How do you solve 15x3−65x2−150x=0?
Solution
Take 5x common and form a quadratic expression inside the bracket. Now, use the middle term split method to factorize the obtained quadratic expression. Substitute each factor equal to 0 one – by – one to get the values of x. The three values of x that will be obtained will be our answer.
Complete step by step answer:
Here, we have been provided with the polynomial expression: 15x3−65x2−150x=0 and we have been asked to solve it. That means we have to find the values of x.
Now, as we can see that we have a cubic polynomial in which the constant term is 0. So, taking 5x common from all the terms, we get,
⇒5x(3x2−13x−30)=0
Dividing both the sides with 5, we get,
⇒x(3x2−13x−30)=0
Now, we have a product of a linear and a quadratic expression, so now we need to find the factored form of 3x2−13x−30. Let us use the middle term split method to do this.
Here, we need to break -13x into two terms such that their product equals the product of the constant term (-30) and +3x2, i.e., −90x2. So, writing 90 as the product of its prime factors, we get,
⇒90=2×3×3×5
So, grouping -18x and 5x, we have,
⇒−18x+5x=−13x and (−18x)×(5x)=−90x2
Therefore, the polynomial expression can be simplified as: -