The graph of the function f(x) is shown below.
When f(x) = 0, x =
- 1.8
- 1.2
0
5
Answers
Given that x = -18, -12, 0 and 5 are the zeros of the equation f(x)
⇒ (x + 18), ( x + 12) ( x + 0) ( x - 5) are the factors of the equation
Find the equation:
f(x) = (x + 18) ( x + 12) ( x + 0) ( x - 5)
f(x) = (x² + 18x + 12x + 216) (x) (x - 5)
f(x) =(x² + 30x + 216) ( x ) ( x - 5)
f(x) =(x³ + 30x² + 216x) ( x - 5)
f(x) = x⁴ + 30x³ + 216x² - 5x³ - 150x² - 1080x
f(x) = x⁴ + 25x³ + 66x² - 1080
Answer: f(x) = x⁴ + 25x³ + 66x² - 1080
Answer:
f(x) is x⁴ + 25x³ + 66x² - 1080
Step-by-step explanation:
In the Given question, the value of x = -18, -12, 0 and 5 and these value are the zeros of the equation f(x).
so the possible factors of the equation
⇒ (x + 18), ( x + 12) ( x + 0) ( x - 5)
Now, you need to find the equation:
f(x) = (x + 18) ( x + 12) ( x + 0) ( x - 5)
by solving equation by multiplying the bracket,
f(x) = (x² + 18x + 12x + 216) (x) (x - 5)
f(x) =(x² + 30x + 216) ( x ) ( x - 5)
f(x) =(x³ + 30x² + 216x) ( x - 5)
f(x) = x⁴ + 30x³ + 216x² - 5x³ - 150x² - 1080x
f(x) = x⁴ + 25x³ + 66x² - 1080
Hence the required function f(x) = x⁴ + 25x³ + 66x² - 1080