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kotegsom [21]
3 years ago
5

172 Eri

Mathematics
1 answer:
AlekseyPX3 years ago
3 0

Answer: 2 roots

Step-by-step explanation:

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3.14159265358979 is the first ten digits of pi.

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Refraise the question
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Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and zeros 3 − 3i and 2, with 2 a
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Answer:

The required polynomial is P(x)=x^4-10x^3+46x^2-96x+72.

Step-by-step explanation:

If a polynomial has degree n and c_1,c_2,...,c_n are zeroes of the polynomial, then the polynomial is defined as

P(x)=a(x-c_1)(x-c_2)...(x-x_n)

It is given that the polynomial R has degree 4 and zeros 3 − 3i and 2. The multiplicity of zero 2 is 2.

According to complex conjugate theorem, if a+ib is zero of a polynomial, then its conjugate a-ib is also a zero of that polynomial.

Since 3-3i is zero, therefore 3+3i is also a zero.

Total zeroes of the polynomial are 4, i.e., 3-3i, 3_3i, 2,2. Let a=1, So, the required polynomial is

R(x)=(x-3+3i)(x-3-3i)(x-2)(x-2)

R(x)=((x-3)+3i)((x-3)-3i)(x-2)^2

R(x)=(x-3)^2-(3i)^2((x-3)-3i)(x-2)^2     [a^2-b^2=(a-b)(a+b)]

R(x)=(x^2-6x+9-9(i)^2((x-3)-3i)(x-2)^2

R(x)=(x^2-6x+18)(x^2-4x+4)                [i^2=-1]

R(x)=(x^2-6x+18)(x^2-4x+4)

R(x)=x^4-10x^3+46x^2-96x+72

Therefore the required polynomial is P(x)=x^4-10x^3+46x^2-96x+72.

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\huge{\boxed{\text{42 ounces}}}

25% is equal to \frac{1}{4}, so multiplying it by 4 gets 100%.  This means we can multiply 10.5 by 4 to get 100% of the fiber the koala ate that day.

10.5*4=\boxed{42}

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