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BabaBlast [244]
1 year ago
9

Three roots of the polynomial equation x4 - 4x3 - 2x2 + 12x + 9 = 0 are 3, -1 and -1. Explain why the fourth root must be a real

number. Find the fourth root.
Mathematics
1 answer:
LiRa [457]1 year ago
3 0
Descares Theorem says that the number of roots of a polynomial is equal to its highest exponent, and the roots could be real and/or imaginary (complex).

However is their is one complex root (a + i.b), it's conjugate is also
a root (a-i.b).

In the equation x⁴ - 4x³ - 2x² + 12x + 9 = 0, we have already 3 roots, then the 4rth cannot be a complex one since we don't have a fifth for its conjugate.

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M∠1=45° and m∠3=65°
7nadin3 [17]

Answer:

In Right Δ ABC with right angle B,

∠A=(3 x -8)°, ∠B=90°, ∠C=(x-2)°

∠A+∠B+∠C=180°[∠ sum property of triangle]

3 x-8+90 + x-2=180

Adding and subtracting like terms

4 x-10+90=180

4 x+80=180

4 x=180-80

4 x=100

x=100/4

x=25°

∠A=3×25-8=75-8=67°




6 0
1 year ago
Read 2 more answers
Under ideal conditions a certain bacteria population is known to double every three hours. Suppose that there are initially 100
lara [203]

Answer:

the estimation of the size of the population after 20 hours is 10159

Step-by-step explanation:

The computation of the size of the population after 20, hours is shown below;

= 100  2^(20 by 3)

= 10159.36

If we divide 20 by 3 so it would give 6.66 that lies between 6 and 7

So the estimation of the size of the population after 20 hours is 10159

hence, the same is relevant

3 0
1 year ago
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On a coordinate plane, a curved line with a minimum value of (negative 1.25, negative 3.25) and a maximum value of (0.25, negati
Talja [164]

Answer: c  

Step-by-step explanation:

its c.

8 0
1 year ago
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Pq=6x+25 and qr=16-3x; find pr
Viktor [21]

Given:\\\overline{PQ}=6x+25\\\overline{QR}=16-3x\\\\Finding:\overline{PR}

If \; Q \; is \; a \; point \; in \; between \; the \; line \; segment \; \overline{PR}, \; \\ then \; the \; distance \; of \; line \; segment \; \overline{PR} \; \\ can \; be \; found \; by \; adding \; line \; segment \; \overline{PQ} \; and \; \overline{QR}.

Using \; the \; concept \; \overline{PQ}+\overline{QR}=\overline{PR} \;,\\ we \; need \; to \; set \; up \; an \; equation \; given \; below:

\overline{PR} =6x+25 +16-3x\\\\Step \; 1: Grouping \; Like \; Terms\\\overline{PR} =6x-3x+25 +16\\\\Step \; 2: Combining \; Like \; Terms\\\overline{PR} =3x+41

Conclusion:

\overline{PR} \; is \; represented \; the \; expression \; 3x +41

3 0
1 year ago
Read 2 more answers
Solve. A power outage affected all homes and businesses within a 3 mile radius of the power station. If the power station is loc
Aneli [31]

Answer:

\left ( x+5 \right )^{2}+\left ( y-6 \right )^{2}= 9

Step-by-step explanation:

The power station is located 5 miles west and 6 miles north of the center of town. So if we try to locate the above points on a Cartesian plane. The co-ordinates of these points will be (-5,6).

And it is also mentioned that a power outage affected all homes and businesses within a 3 mile radius of the power station. So if we plot all the furthest points from the station affected by the power outage it will be a circle of radius 3 miles and center at  (-5,6).

The equation of a circle with center (a,b) and radius r is given by :

\left ( x-a \right )^{2}+\left ( y-b \right )^{2}= r^{2}

Hence the equation of the resulting circle will be: \left ( x+5 \right )^{2}+\left ( y-6 \right )^{2}= 3^{2}

4 0
1 year ago
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