Can someone please help me?

Mathematics

1 answer:

Nana76 [90]3 years ago

5 0

Answer: -5 or -5/1

Step-by-step explanation: Rise over Run

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Find a polynomial function of lowest degree with rational coefficients

xxMikexx [17]

Since -5i is a zero, then its complex conjugate +5i is also a zero of the function.

Therefore,

x + 5i, x - 5i , and x - 3 are factors of the polynomial.

Hence, the polynomial function, P(x), of the lowest degree with rational coefficients is given by

$P(x)=(x+5i)(x-5i)(x-3)$

Which implies that

$\begin{gathered} P(x)=(x^2-(5i)^2)(x-3)=(x^2-25i^2)(x-3) \\ \text{ Since i}^2=-1,\text{ then we have} \\ P(x)=(x-3)((x^2+25)=x^3+25x-3x^2-75 \end{gathered}$

Hence the polynomial is

$P(x)=x^3-3x^2+25x-75$

5 0

1 year ago

If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the va

daser333 [38]

Answer:

a=2

Step-by-step explanation:

Well, first let us find product of the first 8 positive integers, which is 1*2*3*4*5*6*7*8=40320. It can also be written as 40320= $2^{7}$ *3²*5*7. From the formula above, it can be extracted that if a=2, n can be any number from 3 to 7 (considering that a and n are not equal and greater than 1).