Question

If root 5 and minus root 5 are two zeroes of the polynomial x3+3x2-5x-15 find the third zero

Answer 1

Given that $\sqrt{5}, -\sqrt{5}$ are the zeros of given polynomial

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

That means $(x-\sqrt{5}), (x--\sqrt{5})$ are the factors of the given polynomial

multiply both to get another factor

$(x-\sqrt{5}) (x--\sqrt{5})$

$= (x-\sqrt{5}) (x+\sqrt{5})$

$= (x^2+\sqrt{5}x-\sqrt{5}x-(\sqrt{5})^2))$

$= (x^2-5)$

That means $(x^2-5)$ is factor of given polynomial.

Now we will divide $x^3+3x^2-5x-15$ by $(x^2-5)$ to find the third factor

We see that quotient is (x+3)

Hence the third root will be x=-3.

Answer 2

Step-by-step explanation:

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