Mathematics, 22.07.2019 23:00 babbiegirl8035

Which of the following is the complete list of roots for the polynomial function f(x) = (x2 + 2x - 15)(x2 + 8x + 17)? a) -5,3 b) -5,3,-4,+i,-4,-i c) -5,3,-4,+i,4+i d) -4+i , -4 -i

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The first one factors easily. The first quadratic, I mean. The 2 numbers that add up to +2 and at the same time multiply to -15 and 5 and -3. So those are 2 of the 4 roots we have. The second quadratic does not factor so nicely. You need to put that into the quadratic formula to solve. $x= \frac{-8+/- \sqrt{8^2-4(1)(17)} }{2}$ which simplifies to $x= \frac{-8+/- \sqrt{64-68} }{2}$ . That gives us a negative radicand and that's a problem. $x= \frac{-8+/- \sqrt{-4} }{2}$ . Since -1 is equal to i^2, we can rewrite to begin dealing with the negative properly. $x= \frac{-8+/- \sqrt{-1(4)} }{2}$ . Replacing -1 with i^2 gives us $x= \frac{-8+/- \sqrt{i^2(4)} }{2}$ . i^2 has a perfect root of i in it, and 4 has a perfect square of 2 in it, so we simplify more to $x= \frac{-8+/-2i}{2}$ . The 2 in the denominator reduces with the numerator to give us a final 2 roots that are x = -4 + i, and x = -4 - i. Taking all those roots together, we find that the solution to our problem is choice B (although I believe you put some extra commas in there on accident).

Answer from: jahjah1158

Given polynomial function f(x) = (x^2 + 2x - 15)(x^2 + 8x + 17).

In order to find all roots of the given polynomial function, we need to set each of above factor equal to 0.

Therefore,

x^2 + 2x - 15 =0 and x^2 + 8x + 17 =0.

Let us solve first quadratic now.

x^2 + 2x - 15 =0

Factoring out quadratic

(x+5)(x-3) =0

x+5=0 or x-3=0

x=-5 or x=3.

Let us solve second quadratic equation now

x^2 + 8x + 17 =0.

Applying quadratic formula,

$\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x_{1,\:2}=\frac{-8\pm \sqrt{8^2-4\cdot \:1\cdot \:17}}{2\cdot \:1}$

$x=\frac{-8+\sqrt{8^2-4\cdot \:1\cdot \:17}}{2\cdot \:1}:\quad -4+i$

$x=\frac{-8-\sqrt{8^2-4\cdot \:1\cdot \:17}}{2\cdot \:1}:\quad -4-i\$

$x=-4+i,\:x=-4-i$

Therefore, the list of roots for the polynomial function is:

$x=3,\:x=-5,\:x=-4+i,\:x=-4-i.$

So, the correct option is B) -5, 3, -4+i, -4-i.

Answer from: Quest

the correct answer is a) "catholic church".

the proposals that liberals in mexico made during 1855 were particularly focused on a person's individual rights, such as the freedom of speech, the freedom of conscience, freedom of assembly, and the right to possess weapons.

when the constitution was formally published 2 years later (1857). it also contained an article which permitted education free from any religious influence, the removal of the catholic church institutional privileges, and the sale of property belonging to the church. all of these provisions were clearly against the catholic church interests.

Answer from: Quest

it would be a on edgenuit y

the diagram below is your final answer

Which of these triangle pairs can be mapped to each other using a single reflection? ✓

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Which of the following is the complete list of roots for the polynomial function f(x) = (x2 + 2x - 1...