Question

Find the cubic polynomial os zeroes 3,-1,1

Answer 1

Answer:

The required cubic polynomial is $x^3-3x^2-x+3$

Step-by-step explanation:

Concept used:

The cubic polynomial having $\alpha, \:\beta \:and \:\gamma$ as roots is

$x^3-(\alpha+\beta+\gamma)x^2+(\alpha\beta+\beta\gamma+\gamma\alpha)x-\alpha\beta\gamma$

$Given:\\\\\alpha=3,\:\beta=-1,\:\gamma=1\\\\x^3-(\alpha+\beta+\gamma)x^2+(\alpha\beta+\beta\gamma+\gamma\alpha)x-\alpha\beta\gamma\\\\x^3-(3+(-1)+1)x^2+(3(-1)+(-1)1+1(3))x-(3(-1)1)\\\\x^3-3x^2+(-3-1+3)x-(-3)\\\\x^3-3x^2-x+3$

Answer 2

Answer:

x³ - 3x² - x + 3

Step-by-step explanation:

Find the cubic polynomial os zeroes 3,-1,1

3,-1,1 are roots of polynomial

so polynomial would be

(x-3)(x-(-1)(x-1)

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

= (x-3)(x² - 1)

= x³ - x - 3x² + 3

= x³ - 3x² - x + 3