Question

Find all the zeros of the polynomial function f(x) = x + 2x² - 9x - 18 a) (-3) b) (-3. -2,3) c) (-2) d) (-3.2.3) e) none

Answer 1

Answer:x=-3,-2,3

Explanation:

Given equation of polynomial is

`x^(3)+2x^2-9x-18=0`

taking
`x^3` and -9x together and remaining together we get

`x^3-9x+2x^2-18=0`

`x\left ( x^2-9\right )+2\left ( x^2-9\right )`

`x\left ( \left ( x+3\right )\left ( x-3\right )\right )+2\left ( \left ( x+3\right )\left ( x-3\right )\right )`

`taking \left ( x+3\right )\left ( x-3\right ) as common`

`\left ( x+2\right )\left ( x+3\right )\left ( x-3\right )=0`

therefore

x=-3,-2,3