Q:

6. What are the zeroes for thefunctionf(x) = 2x3 + 12x – 10x2?​

Accepted Solution

A:
Answer:x = 0, x = 5 + √13 and x = 5 - √13.Step-by-step explanation:f(x) = 2x^3 + 12x – 10x^2 can and should be rewritten in descending powers of x:  f(x) = 2x^3 – 10x^2 + 12xThis, in turn, can be factored into f(x) = x·(x² - 10x + 12).Setting this last result = to 0 results in f(x) = x·(x² - 10x + 12).Thus, x = 0 is one root.  Two more roots come from x² - 10x + 12 = 0.Let's "complete the square" to solve this equation.Rewrite x² - 10x + 12 = 0  as  x² - 10x +              12 = 0.a) Identify the coefficient of the x term.  It is -10.b) take half of this result:  -5c) square this last result:  (-5)² = 25.d) Add this 25 to both sides of x² - 10x +              12 = 0:      x² - 10x +  25      +      12 = 0 + 25e) rewrite x² - 10x +  25 as the square of a binomial:        (x - 5)² = 13f)  taking the sqrt of both sides:  x - 5 = ±√13g) write out the zeros:  x = 5 + √13 and x = 5 - √13.The three roots are x = 0, x = 5 + √13 and x = 5 - √13.