Question

Obtain all other zeroes of x^4+4x^3 -2x^2- 20x -15, if two of.its zeroes are root 5 and - root 5

Answer 1

Two zeroes are x+√5 and x-√5

(x+√5)(x-√5) = x^2 - 5

Divide x^4+4x^3 -2x^2- 20x -15 by x^2 - 5


The quotient is x^2+4x+3

Now, lets solve x^2+4x+3 = 0

x^2+3x+x+3 = 0
(x+1)(x+3) = 0

So, x = -1 and x= -3 are the other roots of the given equation 

Answer 2

Hey there !!

p(x) = x⁴ + 4x³ – 2x² – 20x – 15

Since two zeroes are √5 and –√5.

= ( x – √5 ) ( x + √5 )

= x² – 5 is a factor of given polynomial.

Refer to the attachment for division.

Now, x² + 4x + 3 = 0

=> x² + x + 3x + 3 = 0

=> x ( x + 1 ) + 3 ( x + 1 ) = 0

=> ( x + 3 ) ( x + 1 ) = 0

=> x + 3 = 0 or x + 1 = 0

=> x = –3 or x = –1

Thus, the zeroes of x⁴ + 4x³ – 2x² – 20x – 15 are √5 , –√5 , –3 and –1.
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Hope my ans.'s helpful. (^-^)