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Your second step is irrelevant asinus!

\((216x^9)^{2/3} \rightarrow(216^{1/3}x^{9\times1/3})^2 \rightarrow (6x^3)^2 \rightarrow 6^2x^{3\times2}\rightarrow 36x^6\)

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Here you need to set the discriminant to be less than zero.

kx^2 +(3-2k)x + k-5 = 0

(3-2k)^2 -4k(k-5) < 0

I'll leave you to work this through.

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(216x^9)^2/3

\(\left(216x^{9} \right) ^{\frac{2}{3} } \) = \(\) \(\sqrt[3]{46656x^{18} } \)  =  \({\color{blue}36x^6}\)

\(\frac{\left(216\times x^{9}\right)^2 }{3} \) = \(\frac{46656x^{18} }{3} = {\color{blue}15552x^{18} }\)

asinus :- )   !

You have found the value of q that gives two equal roots!

For two different real roots your second line should be:  4^2-4(q-2) > 0

This will result in a range of possible q values (q<6 rather than q = 6).

Just substitute the values given into the equation to see if they work.

(You should find C as the result).

General quadratic polynomial:  P(x) = ax^2 + bx + c

P(0) = 1   ⇒   1 =  c

P(1) = 5   ⇒   5 = a + b + c               so 5 = a + b + 1            or   4 = a + b   (1)

P(2) = 11  ⇒  11 = 4a + 2b + c          so 11 = 4a + 2b + 1      or  10 = 4a + 2b  (2)

Multiply (1) by 2 and subtract from from (2) to get:    2 = 2a  or a = 1

Put this back into (1) to get:  4 = 1 + b  or b = 3

So:  P(x) = x^2 + 3x + 1

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What is your question?

Rearrange the equation to look like:

x^2 -2(2k+1)x + k+2 = 0

This has equal roots when the discriminant is zero.

(In general, when a*x^2 + b*x + c = 0, the discriminant is b^2 - 4*a*c): 

(-2(2k + 1))^2 - 4*1*(k+2) = 0

4*(2k+1)^2 - 4*(k+2) = 0

(2k+1)^2 - (k+2) = 0

4k^2 + 4k + 1 - k - 2 = 0

4k^2 + 3k - 1 = 0

(4k - 1)(k + 1) = 0

4k = 1 or k = -1 

k = 1/4 or k = -1

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What do you want to do with this?  Plot it?

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Don't need to be rude!

Thank you melody :D 

8/10

I can't edit the post anymore but the question is what are all the possible values of r that satisfy the equation above?

Nothing was here, stop stalking my profile.

last year, jacob bought a kayak for 670$ . it is know only worth 560% how muck percent did the kayak drop?

I assume your 560% means $560. If so, then:

1 - (560/670) =16.42% drop in kayak's value.

Reggie has 4 dogs on his farm.one dog lark i sabout to have puppies.Write an inequality for the number of dogs reggie will have if lark has fewer than 4 puppies

I assume that      "i sabout"     is meant to be   "is about"  

 Please check your question before you post it.

Reggie has 4 dogs on his farm.

one dog lark is about to have puppies.

Write an inequality for the number of dogs reggie will have if lark has fewer than 4 puppies

reggie will less than 4 dogs assuming that the original 4 and at least on puppy lives.

reggie will have. The most pauppies she will have is 3 so reggie will have no more than 7 altogether.

so he could have       4,5,6,or 7 dogs

\(4\le dogs\le7\\ or\\ 3<dogs<8\\ or\\ 4\le dogs <8\\ or\\ 3<dogs \le 7\)

wht even is scientific notations ............like what do we need this in life for????????????????hmmmmmmmmmmmm......i think tf not you trick a*s teachers

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