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soldier1979 [14.2K]
3 years ago
8

One zero of f(x)=x^3-2x^2-5x+6 is 1 what are other zeros of the function

Mathematics
2 answers:
Alexus [3.1K]3 years ago
8 0

Answer:

-2 and 3

Step-by-step explanation:

Given one zero of f(x)=x^3-2x^2-5x+6 to be 1 this means that x-1 is a factor of the polynomial x³-2x²-5x+6

Before we can get the other two factors. We need to divide the polynomial function by x-1 and factorize the resulting quotient as shown in the attachment.

Quotient Q(x) = x²-x-6

Factorizing this function

x²-3x+2x-6 = 0

x(x-3)+2(x-3) = 0

(x+2)(x-3) = 0

x+2 = 0 and x-3 = 0

x = -2 and x= 3

Therefore the other zeros of the function are -2 and 3

elena-s [515]3 years ago
7 0

Answer:

The other zeros are -2 and 3.

Step-by-step explanation:

As 1 is a zero then (x - 1) is a factor so we divide:

x - 1 )x^3-2x^2-5x+6(x^2-x-6

        x^3-x^2

              -x^2-5x

              -x^2+x

                      -6x+6    

                      -6x+6

                       ...........

x^2 - x - 6 = 0

(x - 3)(x + 2)

x = -2, 3.

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Vadim26 [7]

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This is the fibonacci sequence with each term times x.

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So I said a third term in a consecutive triple of the sequence is equal to the sum of it's two prior terms. Example, f(3)=f(2)+f(1) and f(4)=f(3)+f(2) and so on...

Note, the term before the nth term is the (n-1)th term and the term before the (n-1)th term is the (n-2)th term. Just like before the 15th term you have the (15-1)th term and before that one you have the (15-2)th term. That example simplified means before the 15th term you have the 14th and then the 13th.

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So the full recursive definition is:

f(n)=f(n-1)+f(n-2)

f(1)=1x

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