CPhill

Hard to see this.....but....

AB  = 50    BE = 20    DC   =  35      CA  = 54     DE  =  ????

Triangle ABE  is similar to triangle DCE

So

BE / AB  = EC / DC

20 / 50  =  EC / 35

2 / 5  =  EC   / 35      multiply both sides by  35

( 2/5) * 35  =  14  =  EC

And since 

EC + EA  = AC

14 +  EA  =  54

EA  =  40

And AE / EB   =   DE  /EC

40 / 20  =  DE / 14

2 =  DE /14     multiply both sides by 14

DE  = 28

Remember  that  cos (120)   =   -cos (60)   =  -1/2

So....using the Law of  Cosines

BC^2  =  x^2  + (3x)^2  -  2 (x) (3x) (-1/2)

BC^2   =  x^2  + 9x^2  + 3x^2

BC^2  =  13x^2

BC  = x sqrt (13)

So.....using the Law of Sines

Sin (BCA)  /  x  =  sin (120) / [ x sqrt (13) ]

Sin (BCA)  = sqrt (3)  / [ 2sqrt (13) ] =

Sin (BCA)  =  sqrt (39) / [ 2 * 13 ]  =   sqrt (39) / 26

The stationary point is where the derivative  = 0  [ the graph is "stationary"....neither increasing or decreasing  ]

So.....using rhe quotient rule numerator  [ we needn't worry about the denominator ].........we have

(2x + 4) (x^2 + 4x + 3)  - (x^2 + 4x)(2x + 4)  =  0      factor  and simplify

(2x + 4)  [ 3 ]  =  0

2x + 4    =  0

x  = -2

And y =   [ (-2)^2 + 4*(-2) ] / [ (-2)^2 + 4*(-2) + 3 ] =   -4 / -1  =  4

So...the  "stationary point "  is   ( -2. 4 )

Here's the graph :  https://www.desmos.com/calculator/o8zzqeulqu

The  radius  =   sqrt [ (0 +3)^2  + ( 0 - 4)^2 ] = sqrt [ 9 + 16 ] = sqrt (25)  = 5

So...the equation becomes

(x + 3)^2 + ( y - 4)^2  =  5^2

(x + 3)^2 + ( y - 4)^2  =  25

x * y   =  ( x + 2) (  y - 3)

So

t * ( t + 2)  =

(t  + 2) * [(t + 2) - 3 ]  = 

( t + 2) ( t - 1)

t^2 + t - 2    (1)

  And 

(t + 1) ( t + 1)  =

[ ( t + 1) + 2 ]  *  [ ( t + 1) - 3 ]  =

( t + 3) ( t - 2)  = 

t^2 + t -  6     (2)

So

(1)  - (2)  =

[ t^2 + t  - 2 ]  - [ t^2 + t - 6 ]  =

4

4 is a factor of the numerator: 

x+1 is a factor of the denominator

the numerator has 2 terms

We need to know what the original polynomial is  and what (possible) root we are testing

Just a wild guess....I'd say that  "D" isn't an asset for panel effectiveness

HAHAHA!!!!......this website's info is reliable....well, mostly

"B"  is correct

-15 + 14 - 3 =

-15 +  11  =

- 4    ........ correct !!!