Question

obtain all zeros of the polynomial f(x)= x4-3x3-x2+9x-6 if 2 Of Its zeros -√3 and √3​

Answer 1

Answer:

all zeros of polynomial f(s) are (1, 2, ±√3)

Step-by-step explanation:

f(x)= x⁴ - 3x³ - x² + 9x - 6

If its given zeros are ±√3, then the factors are g(x)

g(x) = (x + √3) (x - √3)

⇒ (x² - 3)

Dividing f(x) by g(x) using long division, we get quotient as

q(x) = f(x) / g(x) = x² - 3x + 2 (see attachment)

Using splitting the middle term for quotient

q(x) = x² - 3x + 2

= x² - 2x - x + 2

= x(x -2) - 1(x - 2)

= (x - 1)(x - 2)

So (1, 2) are other zeros of the polynomial f(x)