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Gala2k [10]
3 years ago
7

What is the least possible degree of a polynomial that has roots -5, 1+4i, and -4i

Mathematics
1 answer:
N76 [4]3 years ago
3 0
If complex coefficients are allowed, the answer is 3.

If the polynomial must have real coefficients, then each complex root comes as a pair of complex conjugate roots.

Root -5 is real, so that is 1 root, and degree 1.

Root 1 + 4i is complex, so it must come with its complex conjugate, 1 - 4i. This adds 2 roots to the polynomial, and now we're up to degree 3.

Root -4i is also complex. It also must come with its complex conjugate, 4i. That adds two more roots, and the degree is 5.

Answer: The least possible degree is 5 with real coefficients.
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3 years ago
A scientist needs 80 liters of a 30% solution of alcohol. She has a 20% solution and a 60% solution available. How many liters o
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60 liters of 20% solution & 20 liters of 60% solution

Step-by-step explanation:

80*0.3=.2x+0.6(80-x)

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2 years ago
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saveliy_v [14]

Answer:

Which question?

Step-by-step explanation:

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3 years ago
What is d+15-9/3+5 PLZZZZZ
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2 years ago
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kicyunya [14]

Answer:

The possible rational roots are: +1, -1 ,+3, -3, +9, -9

Step-by-step explanation:

The Rational Root Theorem tells us that the possible rational roots of the polynomial are given by all possible quotients formed by factors of the constant term of the polynomial (usually listed as last when written in standard form), divided by possible factors of the polynomial's leading coefficient. And also that we need to consider both the positive and negative forms of such quotients.

So we start noticing that since the leading term of this polynomial is x^3, the leading coefficient is "1", and therefore the list of factors for this is: +1, -1

On the other hand, the constant term of the polynomial is "9", and therefore its factors to consider are: +1, -1 ,+3, -3, +9, -9

Then the quotient of possible factors of the constant term, divided by possible factor of the leading coefficient gives us:

+1, -1 ,+3, -3, +9, -9

And therefore, this is the list of possible roots of the polynomial.

6 0
3 years ago
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