Polynomials (C10)

Find all the zeroes of the polynomial 3x4 + 6x3 - 2x2 - 10x - 5 if two of its zeroes are √(5/3) and – √(5/3)

Answer

Since √(5/3) and – √(5/3) are the two zeroes therefore,

(x - √(5/3))(x + √(5/3)) = 1/3(3x2 - 5) is a factor of given polynomial.

Divide the given polynomial by 3x2 – 5.

For other zeroes, x2 + 2x + 1 = 0

(x + 1)2 = 0

x = –1, –1

Zeroes of the given polynomial are √(5/3), – √(5/3), –1 and –1.