Question

find all the zeroes of the polynomial f(x) = x^4+x^3-23x-3x+60, if it is given that two of its zeroes are 5 and 4​

Answer 1

Answer:

(x - root3)*(x + root3) is one factor

By using identity

(x^2 - 3) is one factor

x^4 + x^3 - 23x^2 - 3x + 60 / x^2 - 3

= x^2 + x - 20

The zeroes of x^2 + x - 20 are -5 and 4

All the zeroes of the given polynomial are

root3, -root3, -5, 4

Answer 2

Answer:

Hii

Let f(x) = x4 + x3 – 23x2 – 3x + 60. Since √3 and –√3 are the zeroes of f(x), it follows that each one of (x – √3) and (x + √3) is a factor of f( x).