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1) Find all the zeros of the function: g(x)= x^3+3x^2-18x-40, given that one factor is (x+5) 2)Find all zeros of the function: g(x)= x^3+x^2-17x+15, given that one zero is x=1

User Kel
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It is given that


g(x)=x^3+3x^2-18x-40

The one factor of g(x) is (x+5).

By using the synthetic method, we get


g(x)=(x+5)(x^2-2x-8)


g(x)=(x+5)(x^2-4x+2x-8)


g(x)=(x+5)(x(x-4)+2(x-4))


g(x)=(x+5)(x-4)(x+2)

Hecne zeros of g(x) is -5,4, and -2.

2)

It is given that


g(x)=x^3+x^2-17x+15

The one zero of the given g(x) is x=1.

By using the synthetic method, we get


g(x)=(x-1)(x^2+2x-15)


g(x)=(x-1)(x^2+3x-5x-15)


g(x)=(x-1)(x(x+3)-5(x+3))


g(x)=(x-1)(x+3)(x-5)

To find zeros of g(x) by equating g(x) to zero.


g(x)=(x-1)(x+3)(x-5)=0


(x-1)=0;(x+3)=0;(x-5)=0


x=1;x=-3;\text{ x=5}

Hence the zeros of the given function g(x) are 1,-3, and 5.

1) Find all the zeros of the function: g(x)= x^3+3x^2-18x-40, given that one factor-example-1
1) Find all the zeros of the function: g(x)= x^3+3x^2-18x-40, given that one factor-example-2
User Czechboy
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