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n200080 [17]
3 years ago
7

a(t)=(t−k)(t−3)(t−6)(t+3) is a polynomial function of tt, where kk is a constant. Given that a(2)=0a(2)=0, what is the absolute

value of the product of the zeros of aa? Answer:
SAT
1 answer:
Snowcat [4.5K]3 years ago
3 0

Answer:

The absolute value of the product of the zeros of a(t) is 108.

Step by step explanation:

The given polynomial function is

a(t)=(t-k)(t-3)(t-6)(t+3)

Where k is the constant.

To find the zeros of a(t), equate the polynomial equal to zero.

(t-k)(t-3)(t-6)(t+3)=0

By using zero product property, equate each factor equal to zero.

t-k=0

t=k

t-3=0

t=3

t-6=0

t=6

t+3=0

t=-3

Therefore the zeros of the function are k, 3, 6 and -3. Since it is given that

a(2)=0

Therefore, 2 is a zero of a(t). So, the value of k is 2.

The product of zeros is

2\times 3\times 6\times -3=-108

The absolute value of the product is 108.

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