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erik [133]
3 years ago
14

At most, how many unique roots will a third-degree polynomial function have?

Mathematics
1 answer:
beks73 [17]3 years ago
7 0

The fundamental theorem of algebra states that a polynomial with degree n has at most n solutions. The "at most" depends on the fact that the solutions might not all be real number.

In fact, if you use complex number, then a polynomial with degree n has exactly n roots.

So, in particular, a third-degree polynomial can have at most 3 roots.

In fact, in general, if the polynomial p(x) has solutions x_1,\ x_2,\ldots x_n, then you can factor it as

p(x) = (x-x_1)(x-x_2)\ldots (x-x_n)

So, a third-degree polynomial can't have 4 (or more) solutions, because otherwise you could write it as

p(x)=(x-x_1)(x-x_2)(x-x_3)(x-x_4)

But this is a fourth-degree polynomial.

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E. Sandy’s monthly bank statement showed the following deposits and withdrawals: -$14.10, $41.50, -$11.03, -$7.25, $83.22 If San
storchak [24]

Answer:

$149.09

Step-by-step explanation:

56.75-14.10=42.65

42.65+41.50=84.15

84.15-11.03=73.12

73.12-7.25=65.87

65.87+83.22=149.09

5 0
2 years ago
HELPPP!!!
xxMikexx [17]

The angles ∠CFE and ∠AFB are vertically opposite angles. Then the value of x will be 6.

<h3>What is an angle?</h3>

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

We know that the angle ∠DFE is 90°.

Then the sum of the angle ∠CFD and ∠DFE will be

∠CFD + ∠DFE = 27° + 90°

∠CFD + ∠DFE = 117°

Then the angles ∠CFE and ∠AFB are vertically opposite angles. Then we have

∠CFD = ∠DFE

Put the values

21x - 9 = 117

    21x = 126

        x = 6

More about the angled link is given below.

brainly.com/question/15767203

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8 0
2 years ago
Tyler’s brother earns a commission. He makes 2.5% of the amount he sells. Last week, he sold $900 worth of shoes. How much was h
lukranit [14]

Answer:

$22.5

Step-by-step explanation:

2.5% of 900

0.025(900)= 22.5

7 0
3 years ago
Geoff paddles his canoe at an average speed of 3.5 miles per hour. After 5 hours of canoeing, Geoff has traveled 18 miles. Write
andriy [413]

Answer:

d(x) = 3.5x + 0.5

Step-by-step explanation:

3.5 x 5 = 17.5 which means the canoe began from a starting point of 0.5

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2 years ago
2. Which expression is equivalent to 3ly-6)?
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pyfoydoye9ye9ye9ts8ts9teo5e

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