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

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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Can someone help me with number 50?

timama [110]

Let's take a peek at the denominators first off, and do a "prime factoring" on them.

25 = 5 * 5

27 = 3 * 3 * 3

45 = 3 * 3 * 5

the numbers in bold are repeated there more than once among the factors, and therefore we'll use them once, so our LCD will be 5 * 5 * 3 * 3 * 3, or 675.

$\bf \stackrel{Alaska}{\cfrac{4}{25}}~+~\stackrel{Texas}{\cfrac{2}{27}}~+~\stackrel{California}{\cfrac{2}{45}}~~ \stackrel{LCD~675}{\implies }~~ \cfrac{(27)4~+~(25)2~+~(15)2}{675}
\\\\\\
\cfrac{108+50+30}{675}\implies \cfrac{188}{675}$

3 0

3 years ago

If 7.5% of pizza orders in gotham are for hawaiian pizzas, and you know that there are 100 pizza restaurants in gotham, what can

LUCKY_DIMON [66]

Answer: There are approximately 8 restaurants that have hawaiian pizzas on their menus.

Step-by-step explanation:

Total number of pizzas restaurants in Gotham = 100

Percent of pizza orders in Gotham are for hawaiian pizzas = 7.5

Number of Gotham restaurants that have hawaiian pizzas on their menus is given by

$7.5\%\text{ of} 100\\\\=\frac{7.5}{100}\times 100\\\\=7.5$