Question

pleaaase help.... fan and medals

question in comments

Answer 1

@Michele_Laino

Answer 2

I call with F(x) the subsequent function:
\[F\left( x \right) = {\left( {x - 2} \right)^2}g\left( x \right)\]
then, applying the product rule, we can write the first derivative of F(x) as below:
\[F'\left( x \right) = 2\left( {x - 2} \right)g\left( x \right) + {\left( {x - 2} \right)^2}g'\left( x \right)\]
now please try to factor out x-2, what do you get?

Answer 3

thank you.. got it.. it was so easy

Answer 4

I'm working on question #2, please wait...

Answer 5

yes

Answer 6

here we can write this:
\[{x^5} + a{x^4} + 3{x^3} + b{x^2} + a = P\left( x \right){\left( {x - 2} \right)^2}\]
according to the hypothesis of your problem

Answer 7

where P(x) is another polynomial.
Now if I replace x with 2, I substitute x=2 into that equation, what do you get?

Answer 8

this will be equal to 0

Answer 9

hint:
the right side is:
\[P\left( 2 \right){\left( {2 - 2} \right)^2} = 0\]

Answer 10

please write the left side after that substitution

Answer 11

hint:
we have:
\[{2^5} + a \times {2^4} + 3 \times {2^3} + b \times {2^2} + a = 0\]
please simplify

Answer 12

32+16a+24+4b+a = 0

Answer 13

then you can simplify further:
what is 32+24=...
what is 16a+a=...

Answer 14

56 and 17a

Answer 15

i ve understood it now.. can work it/// thank you so much for your help

Answer 16

ok! so we got this condition or equation:
\[56 + 17a + 4b = 0\]

Answer 17

:)