how do i solve part 5b without using polymers or the cubic formula ?
#i need help Asap
karmic saddle
stiff pythonBOT
how do i solve part 5b without using polymers or the cubic formula ?
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gloomy canopy
how do i solve part 5b without using polymers or the cubic formula ?
huh?
karmic saddle
how do i solve part be
karmic saddle
what kind of emoji pfp is that?
that doesnt matter
gloomy canopy
i cant help you i am sorry
karmic saddle
ohh okay
urban hornet
What does it mean for an equation to have a tangent? What are the requirements for the tangent line?
karmic saddle
What does it mean for an equation to have a tangent? What are the requirements f...
like the line on a curve
like the red line
urban hornet
like the red line
Yes, but what conditions does this impose on the tangent line?
karmic saddle
I don't know tbh
gloomy canopy
how do i solve part 5b without using polymers or the cubic formula ?
hi taffy
karmic saddle
Hi
urban hornet
I don't know tbh
What does it mean for something to be tangent to something else?
sleek vale
Bro the answer of b is?
urban hornet
First you need a
urban hornet
Why are you throwing around answers man
Don't be like that. The person asking is learning
urban hornet
?tag help
rose moonBOT
sleek vale
For a) part id say differentiate the equation by which you will get the dy/dx and put x = 1 which will get you the slope of the tangent
then using y =mx +c you can find the equation putting the values
NOW FOR PART B
THIS IS WHAT I DID I AM NOT SURE OF HOW CORRECT IT IS
Keep the dy/dx = slope which coming out to be 4
then you will get two values of x
solving the quadratic
one will be 1
and then take the other value and put that in y = 4x + 1
youll get the y coordinate with respect to the second value
(NVM ITS WRONG JUST REALISED)
sleek vale
I have one more solution
equal the tangent to the curve
and then
Take the roots as A,B,C
then A+B+C = -(coeff of x^2)/coeff of x^3
take any one root to be 1
like this youll get the equations
and fine the roots and put its value in the curve to get y
the answer is coming -1.5,-5
urban hornet
What does it mean for two equations to be equal to each other? Hint: what sort of root are you taking
And what does a root of a polynomial mean wrt factoring it?
karmic saddle
Take the roots as A,B,C
could you write down the full equation. I'm struggling to visualise
frozen tiger
take any one root to be 1
@karmic saddle I will help explain why this is true
As CosmicMan said, we equate the formulae of the y-coordinates of the curve and the tangent line to find their intersections
2x^3 - x^2 + 4 = 4x + 1
2x^3 - x^2 - 4x + 3 = 0
The sum of the coefficients of 2x^3 - x^2 - 4x + 3 is 0, which means 2x^3 - x^2 - 4x + 3 evaluated at 1 has value 0.
This implies that x - 1 is a factor of 2x^3 - x^2 - 4x + 3, by factor theorem.
Then you may feel free to continue on CosmicMan's steps, or even take long division between 2x^3 - x^2 - 4x + 3 and x - 1 and proceed to factorize the quotient, which is quadratic
urban hornet
2x^3 - x^2 + 4 = 4x + 1
2x^3 - x^2 - 4x + 3 = 0
The sum of the coefficients of 2...
No reason to do this work though, as the question a) already told us that x=1 was a root of their difference.
But it is a useful thing to check when going over roots of polynomials
frozen tiger
No reason to do this work though, as the question a) already told us that x=1 wa...
Ah, very true
karmic saddle
@frozen tiger I understand what youre saying right but how to i factorise without using long division
frozen tiger
<@195844111050211330> I understand what youre saying right but how to i factoris...
As CosmicMan suggested, you can solve for the roots using Vieta's formulae:
https://en.wikipedia.org/wiki/Vieta's_formulas
frozen tiger
Hmm i have different approach for B
How did you get the factors x + 1 and 2x + 3?
urban hornet
One of those factors is incorrect the others are correct
sleek vale
One of those factors is incorrect the others are correct
nope except 1 both are incorrect
frozen tiger
2x + 3 and substituting -2/3 lolz
mighty niche
nope except 1 both are incorrect
ooh lol.. how the hell i got these factors 🫢
mighty niche
EDITT:
Sorry the last step of factorisation is incorrect.
The correct factors are (x-1)(x-1)(2x+3)
mint depot
how do i solve part 5b without using polymers or the cubic formula ?
find the derivative and value of $2x^3 - x^2 + 4$ at $x = 1$ and check if they agree with $y = 4x + 1$
sweet gustBOT
赤色のシャナ
mint depot
that's basically it
the explanation is that tangent lines have a specific condition that they need to satisfy that forces them to have the same slope as is the derivative of the curve at the point it is tanget to.
in other words, it's basically how the derivative works. think about it
frozen tiger
find the derivative and value of $2x^3 - x^2 + 4$ at $x = 1$ and check if they a...
Why x = 5, and why does the derivative need to agree with that of the straight line? The question seems to only require the curve and the straight line meet elsewhere