Prelim 2016 Maths Help Thread (1 Viewer)

[Orwell]

eyeseeyou is one of those people that really, really needs to think before he posts. All his comments and remarks have been subject to roasting (looking @ Nailgun lmao).

 

[Nailgun]

eyeseeyou is one of those people that really, really needs to think before he posts. All his comments and remarks have been subject to roasting (looking @ Nailgun lmao).

 

[Green Yoda]

When it says 2 roots differ by 4, does it mean that the roots are x and x+4 or x and x-4?

 

[Nailgun]

When it says 2 roots differ by 4, does it mean that the roots are x and x+4 or x and x-4?

same thing, you've just switched them around

if roots are 2 and 6

if we take 2 as x

x, x+4

if we take 6 as x

x, x-4

 

[Green Yoda]

same thing, you've just switched them around

if roots are 2 and 6

if we take 2 as x

x, x+4

if we take 6 as x

x, x-4

for one of the questions, I did x and x-4 and it didnt work but x and x+4 worked

 

[Suu]

for one of the questions, I did x and x-4 and it didnt work but x and x+4 worked

Could you post the question here?

 

[Green Yoda]

Find p if the roots of an equation 3x^2+px-12=0 differ by 4.

 

[si2136]

Usually you do x, x+4. For example, difference between roots are 19, it would usually be x, x+19.

 

[leehuan]

Find p if the roots of an equation 3x^2+px-12=0 differ by 4.

Assume that the roots of the polynomial equation are (a-4) and a

Because that's what you got stuck on.


From the product of roots: a(a-4) = -4
i.e. a^2 - 4a + 4 = 0
(a-2)^2 = 0
a = 2

From the sum of roots:

a + (a-4) = -p/3

2 + (-2) = -p/3
p = 0

 

[leehuan]

Now assume the roots of the polynomial equation are a and (a+4)

From the product of roots: a(a+4) = -4
i.e. a^2 + 4a + 4 = 0
(a+2)^2 = 0
a = -2

From the sum of roots:

(a+4) + a = -p/3

-2+4 - 2 = -p/3

p = 0
_____________________

Check:

When p=0, we have

3x^2 - 12 = 0

x^2 - 4 = 0

x = -2, x = 2
Clearly, the roots differ by 4

 

[Green Yoda]

Nvm made a fkin silly mistake omg

 

[Green Yoda]

Another question:
Find the equation of a parabola through the points (2,0),(4,0)and(0,8)

 

[Suu]

Another question:
Find the equation of a parabola through the points (2,0),(4,0)and(0,8)

(2,0) and (4,0) will be the x-intercepts. (0,8) shows that it crosses the y intercept at 8, and therefore is concave up. Can you go from there?

 

[Green Yoda]

(2,0) and (4,0) will be the x-intercepts. (0,8) shows that it crosses the y intercept at 8, and therefore is concave up. Can you go from there?

Yeah, I have inspected that but I don't know how to put in the general form.

 

[Suu]

Yeah, I have inspected that but I don't know how to put in the general form.

Find -b and c from the roots that were provided (2, and 4). (hint: assume a=1)
(second hint: use the root formulas!)
(third hint: if c/a = y int when x=0, you are probably on the right track)

 

[DatAtarLyfe]

Alternatively, you could use the fact that
f(x) = a(x - 2)(x - 4) [from the x-intercepts], where a is the real, leading, unknown coefficient of the quadratic. Then just expand and let x = 0, y = 8 to find a.

 

[KingOfActing]

Another question:
Find the equation of a parabola through the points (2,0),(4,0)and(0,8)

The equation will be of the form since 2 and 4 are the roots. Substituting x = 0, y = 8 gives a = 1 so the equation is and you can expand that if you want.

 

[leehuan]

Alternatively, you could use the fact that
f(x) = (ax - 2)(x - 4) [from the x-intercepts], where a is the real, leading, unknown coefficient of the quadratic. Then just expand and let x = 0, y = 8 to find a.

Don't you mean f(x) = a(x-2)(x-4) (edit: as KoA said)

Because you're implying there that a root is at x=2/a

 

[Trebla]

When you took the square root, why did you choose the positive and not the negative one? Think about which one makes sense given the condition imposed.

eyeseeyou, you still haven't answered my question above. Please stop avoiding my questions and answer my question above and the questions below thank you.

I only lookied at it for like 5 seconds b/c I didn't have the time to fully look at it

BTW leehuan

I found out the trig derivation: https://en.wikipedia.org/wiki/Proofs_of_trigonometric_identities

Why did you feel the need to ask it here then if you already knew it was there in a textbook or out there on the internet?

Well you can't really say things unless you've done/experienced it b4

E.g. I hate doing modern history. I've never experienced that before however it seems like a boring subject which I would hate as I have done some sort of modern history in the past. You get what I mean

4U maths is on a different tangent to 2u maths (considering the scaling)

In that case why did you feel the need to tell some tutors how to do their job when you haven't tutored anyone yourself?

 

[DatAtarLyfe]

Don't you mean f(x) = a(x-2)(x-4) (edit: as KoA said)

Because you're implying there that a root is at x=2/a

Yep my bad.