Question

find all the zeroes of x^4+4x^3-2x^2-20x-15 having two of its zeros are √5 and -√5

Answer 1

Hii friend,

P(X) = X⁴+4X³-2X²-20X-15

✓5 and -✓5 are the zeros of the P(X)

(X-✓5) (X+✓5) are the factor of the P(X).

(X)² - (✓5)² = X²-5.

G(X) = X²-5

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

Remainder = 0

Quotient = X²+4X+3

Factories the Quotient then we will get other zeros of the polynomial X⁴+4X³-2X²-20X+5

=>X²+4X+3

=> X²+3X+X+3

=> X(X+3) +1(X+3)

=> (X+3) (X+1)

=> X+3 = 0. OR X+1 = 0

=> X= -3 OR X = -1

Hence,

-3 , -1 , ✓5 and -✓5 are the four zeros of the polynomial X⁴+4X³-2X²-20X-15.


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