Question

let f(x) = x^3+3x^2-x-3. Find the polynomial function each of whose roots are two less than the roots of f(x)​

Answer 1

Explanation:

f(x) = x³ + 3x² - x - 3 = x²(x + 3) - (x + 3)

= (x² - 1)(x + 3) = (x + 1)(x - 1)(x + 3).

The roots of f(x) are x = -3, -1 and 1.

=> The new roots are x = -5, -3 and -1.

=> g(x) = (x + 5)(x + 3)(x + 1) = x³ + 9x² + 23x + 15.