2 years ago

Which statement correctly describes the end behavior of the function f ( x ) = − x 2 + 3 x + 12

Mathematics

1 answer:

Yuri [45]2 years ago

8 0

X—>-infinity f(x)—>-infinity
X—>infinity f(x)—> 12

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Write the general polynomial p(x) if its only zeros are 1 4 and -3 with multiplicites 3 2 and 1 respectively what is the degree

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Answer:

The 6th degree polynomial is $p(x) = (x-1)^3(x-4)^2(x+3)$

Step-by-step explanation:

Zeros of a function:

Given a polynomial f(x), this polynomial has roots $x_{1}, x_{2}, x_{n}$ such that it can be written as: $a(x - x_{1})*(x - x_{2})*...*(x-x_n)$ , in which a is the leading coefficient.

Zero 1 with multiplicity 3.

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Zero 4 with multiplicity 2.

Considering also the zero 1 with multiplicity 3.

$p(x) = (x-1)^3(x-4)^2$

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Considering the previous zeros:

$p(x) = (x-1)^3(x-4)^2(x-(-3)) = (x-1)^3(x-4)^2(x+3)$

Degree is the multiplication of the multiplicities of the zeros. So

3*2*1 = 6

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