AMEN.. Discriminant, Delta help i am suffering... (4 Viewers)

[HeroicPandas]

Can someone PLEASE explain to me the difference between:



and



BEFORE u say anything, i know that when there is exactly 1 root

 

[asianese]

2 REAL ROOTS

REAL ROOTS ( one OR two)

 

[HeroicPandas]

2 REAL ROOTS

REAL ROOTS ( one OR two)

EXACTLY 2 roots??

one OR two roots, SO IT DOESNT EXCEED 2

 

[asianese]

OH EXXXXACTLY.

Wtf we're talking about quadratics I'm assuming? Maximum roots for ANY quadratic is 2 roots.

 

[asianese]

Also just to confuse you when the (2) roots are rational.

 

[asianese]

Btw it'd be good if you actually respond quickly so we get the matter sorted

 

[HeroicPandas]

Ok here is a random question:

- A cubic function is given with an unknown value of k for eg. <----- random function i made up
- It asks to factorise given a root
- "Find the values of k, if this cubic function has exactly 3 roots"

And when u factorise u something like this :

Then we use quadratic formula to solve the quadratic in the 2nd bracket

here is my problem i used but the answer says i have to use

 

[HeroicPandas]

Also just to confuse you when the (2) roots are rational.

Not confused, I know this

 

[HeroicPandas]

OH EXXXXACTLY.

Wtf we're talking about quadratics I'm assuming? Maximum roots for ANY quadratic is 2 roots.

Yes quadratics

 

[deswa1]

If the discriminant is greater than or equal to zero, it will have two real roots. Always use this unless you know that the roots are distinct

 

[asianese]

For the cubic question I think you need to consider stationary points and whether they lie above or below the x axis. There is no discriminant theory for cubic in the HSC syllabus.

Also x^2-3x+5 discriminant is -11 so immediately you know it has no real roots.

 

[HeroicPandas]

For the cubic question I think you need to consider stationary points and whether they lie above or below the x axis. There is no discriminant theory for cubic in the HSC syllabus.

Also x^2-3x+5 discriminant is -11 so immediately you know it has no real roots.

amen... the cubic info is used to guide u to where my problem is,

my problem is the quadratic part to find the values of k for when that quadratic has 2 DIFFERENT roots

 

[HeroicPandas]

If the discriminant is greater than or equal to zero, it will have two real roots. Always use this unless you know that the roots are distinct

Distinct means different?

 

[HeroicPandas]

If the discriminant is greater than or equal to zero, it will have two real roots. Always use this unless you know that the roots are distinct

"If the discriminant is greater than or equal to zero, it will have two real roots" CAN THESE ROOTS BE the SAME? or can they be DIFFERENT?

 

[asianese]

THEY CAN BE EITHER THE SAME OR DIFFERENT.

Two real roots: any two real numbers e.g. 2, 3, (x-2)(x-3)=x^2-5x+6 or 2, 2 (x-2)^2 = x^2-4x+4

 

[deswa1]

Ok- A quadratic either has TWO real roots or NO real roots- it can't have just one. If the discriminant (D) is GREATER THAN OR EQUAL TO zero, then it will have two real roots. If it is less than zero, it will have no real roots. If and only if the discriminant is equal to 0, the two roots will be the same.

So:

D>=0 -> two real roots
D>0 -> two real roots that ARE NOT the same
D=0 -> two real roots that ARE the same
D<0 -> no real roots

Make sense?

 

[asianese]

^ This.

 

[HeroicPandas]

THEY CAN BE EITHER THE SAME OR DIFFERENT.

Two real roots: any two real numbers e.g. 2, 3, (x-2)(x-3)=x^2-5x+6 or 2, 2 (x-2)^2 = x^2-4x+4

"THEY CAN BE EITHER THE SAME OR DIFFERENT"

ARE U TALKING about DELTA GREATER or equal to zero?

 

[asianese]

D implies D = 0 OR D > 0

For D=0, same root
D>0, different root

 

[HeroicPandas]

Ok- A quadratic either has TWO real roots or NO real roots- it can't have just one. If the discriminant (D) is GREATER THAN OR EQUAL TO zero, then it will have two real roots. If it is less than zero, it will have no real roots. If and only if the discriminant is equal to 0, the two roots will be the same.

So:

D>=0 -> two real roots
D>0 -> two real roots that ARE NOT the same
D=0 -> two real roots that ARE the same
D<0 -> no real roots

Make sense?

D>=0 -> two real roots
D>0 -> two real roots that ARE NOT the same
D=0 -> two real roots that ARE the same
D<0 -> no real roots

I get the ones in bold,
"D>0 -> two real roots that ARE NOT the same" THIS MEANS 2 REAL ROOTS THAT ARE DISNTINCT/different?

D>=0 -> two real roots

2 real roots that can be the SAME? and be DIFFERENT ( U ONLY USE THIS WHEN u dont know if the 2 roots u are finidng are diffferent)