Question

Given that x - root 5 is a factor of the polynomial x3 - 3 root 5x2 - 5x + 15 root 5, find all the zeroes of the polynomial.

Answer 1

Hii friend,

(X-✓5) is a factor of the polynomial X³-3✓5X²-5X+15✓5.

G(X) = (X-✓5)

P(X) = X³-3✓5X²-5X+15✓5.

On dividing P(X) by G(X) we get,

Quotient = X²-2✓5-15X².

And,

Remainder = 0

Factories the Quotient then we will get the two other zeros of the P(X).

Quotient = X²-2✓5X-15

=>X²-3✓5X+✓5X-15

=> X(X-3✓5) +✓5(X-3✓5)

=> (X-3✓5) (X+✓5)

=> (X-3✓5) = 0 Or (X+✓5) = 0

=> X = 3✓5 or X = -✓5.

Hence,

3✓5 , -✓5 are the two other zeros of the polynomial X³-3✓5X²-5X+15✓5

HOPE IT WILL HELP YOU..... :-)