Question

If ±√5 are the two zeros of the polynomial p(x)=x^3+3x^2-5x-15 , then find the third zero.​

Answer 1

Answer:

Step-by-step explanation:

Hello !!!

Here, x^3 +3x^2 -5x -15 = 0 is the given polynomial.

The two zeroes = √5 and -√5

x^3 + 3x^2 - 5 x - 15

= √5 -√5

= (x-√5) (x+√5)

= x^2 + √5x - √5x -5

= x^2 - 5

Now Dividing we get,

x^2 - 5 ) x^3 + 3x^2 - 5x - 15 ( x + 3

x^3 - 5x

- +

---------------------------------

3x^2 - 15

3x^2 - 15

- +

---------------------------------

0

Hence your third zero = x = -3

I hope it help you.

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