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3 years ago

If a polynomial with real coefficients is of degree 3. Can we say there must be at least 1 real root?

Mathematics

1 answer:

Shalnov [3]3 years ago

8 0

Answer:

A polynomial of degree 3 has 3 linear factors… (1): (x - i ) (x + i ) (x + a) . If any 2 factors are conjugate as here first 2 factors are conjugate with complex roots. So at least one root should be real.

Step-by-step explanation:

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In the kite , AK=9 , JK=15 , and AM=16 .

Veronika [31]

Answer:

The Length of JM is 20.

Step-by-step explanation:

Given,

JKLM is a kite in which JL and KM are the diagonals that intersect at point A.

Length of AK = 9

Length of JK = 15

Length of AM = 16

Solution,

Since JKLM is a kite. And JL and KM are the diagonals.

And we know that the diagonals of a kite perpendicularly bisects each other.

So, JL ⊥ KM.

Therefore ΔJAK is aright angled triangle.

Now according to Pythagoras Theorem which states that;

"The square of the hypotenuse is equal to the sum of the square of base and square of perpendicular".

$JK^2=KA^2+AJ^2$

On putting the values, we get;

$(15)^2=9^2+AJ^2\\\\225=81+AJ^2\\\\AJ^2=225-81=144$

On taking square root onboth side, we get;

$\sqrt{AJ^2} =\sqrt{144}\\\\AJ=12$

Again By Pythagoras Theorem,

$AJ^2+AM^2=JM^2$

On putting the values, we get;

$JM^2=(12)^2+(16)^2\\\\JM^2=144+256=400$

On taking square root onboth side, we get;

$\sqrt {JM^2}=\sqrt{400}\\\\JM=20$

Hence The Length of JM is 20.

4 0

3 years ago

A coffee pot holds 5 1/2 quartz of coffee. How much is his in cups?

pav-90 [236]

12 1/2 cups is equavelent

6 0

2 years ago

Distance between two points (-5,5) and ( 3,-3)

stiks02 [169]

Answer:

$8\sqrt{2}$

Step-by-step explanation:

Using the pythagorean theorem, you can find that the distance between the two points is $\sqrt{(3-(-5))^2+(5-(-3))^2}=\sqrt{128}=8\sqrt{2}$ . Hope this helps!

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3 years ago

You deposit $10,000 in a money-market account that pays an annual interest rate of 4.4%. The interest is compounded quarterly. H

sergiy2304 [10]

Total = principal * (1 + rate/n)^n*years
where "n" is the number of compounding periods per year
Total = 10,000 * (1 + .044/4)^4*2
Total = 10,000 * (1.011)^8
Total = 10,000 * 1.0914635699 
Total = 10,914.64

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3 years ago

Which of the following has the greatest value A)3³ B)5² C)1¹⁰ D)2⁵

Alecsey [184]

Answer:

A - Highest is 27

Step-by-step explanation:

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7 0

3 years ago

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