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 functions are

h(x) = 3x + 2

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values of k (x)

case 1) k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option 4. k(x) = 2^(3x + 2 )

case 2) k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option 1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) = [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option 3.) k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) = [2^x]-[3x + 2]=2^x-3x-> is the option 2.) k(x) = 2^x - 3x - 2

case 5) k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option 5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option 6. k(x) = 3(2^x) +2

Answer from: Quest

to determine the unit cost your would divide the total cost by the number sold.

7 bagels for $4.41 $4.41/7 = $.63 each at fresh side

5 bagels for $3.60 $3.60/5 = $.72 each at value mart

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