Discriminat-?! (2 Viewers)

[epicFAILx]

I was understanding things in maths until.. *dramatic music* the discriminative.

PLEASE EXPLAIN :/

 

[slyhunter]

If you're referring to the discriminant, then it's the stuff under square root in the quadratic formula.

 

[epicFAILx]

how does it work?

im really confuzzled :S

 

[Alkanes]

What are you finding hard about it? It's basically a part of the quadratic formula

 

[The Derivative]

if itz gratur den zer0, den there iz 2 s0lutionz 4 x.
Id itz less den zer0, it has one or no solutionz or sumting lyk dat idk.

Amiright? lol
~tbh, I have nfi

 

[Alkanes]

speak english

 

[funnytomato]

you can associate "discriminant" with the meaning of discriminating(distinguishing)

basically it tells the difference bewteen quadratics (actually polynomials of any degree, which you don't need to worry about)

when it's larger/equal to zero, the quadratic has real roots
when it's smaller than zeor, it has no real roots

 

[The Derivative]

you can associate "discriminant" with the meaning of discriminating(distinguishing)

basically it tells the difference bewteen quadratics (actually polynomials of any degree, which you don't need to worry about)

when it's larger/equal to zero, the quadratic has real roots
when it's smaller than zeor, it has no real roots

I basically said the same thing. haha

 

[funnytomato]

What are you finding hard about it? It's basically a part of the quadratic formula

+1
it's related to the quadratic formula (which is derived from completing the square of the general equation of a quadratic ax^2 + bx + c= 0)

the solutions of ax^2 + bx + c= 0 are x= (-b+ sqrt(b^-4ac)) / 2a or x= (-b-sqrt(b^-4ac)) / 2a

so we'll need to find square root of a negative number if discriminant (b^-4ac) is smaller than 0, which doesn't exist in real numbers , so the quadratic has no real roots

otherwise, it has 2 real roots (which are obviously equal to each other when discriminant is 0)

 

[funnytomato]

I basically said the same thing. haha

speak english

..

 

[SpiralFlex]

Let's see a basic quadratic function of:



We all know what the quadratic formula is right?



Now, we call the discriminant the part under the square root.



So what if this "discriminant" is positive?

That is,



We get two different real solutions!

So what if the "discriminant" is equal to zero?

That is,



We get two equal real solutions!

So what if the "discriminant" is less than zero?

That is,



Since the discriminant is a negative when it is less than zero, and a square root of a negative number has no real solutions. We say it has no real solutions!

Try it yourself!

Use the normal way of solving it, then see how many solutions.

Then see if it matches with the discriminant.

Do the same with (for epicFAILx only):

a)

b)

c)

PM me for a list of exercises.

Note we usually call the discriminant . (Captial Greek letter for D.)

So

 

[epicFAILx]

Let's see a basic quadratic function of:



We all know what the quadratic formula is right?



Now, we call the discriminant the part under the square root.



So what if this "discriminant" is positive?

That is,



We get two different real solutions!

So what if the "discriminant" is equal to zero?

That is,



We get two equal real solutions!

So what if the "discriminant" is less than zero?

That is,



Since the discriminant is a negative when it is less than zero, and a square root of a negative number has no real solutions. We say it has no real solutions!

Try it yourself!

Use the normal way of solving it, then see how many solutions.

Then see if it matches with the discriminant.

Do the same with (for epicFAILx only):

a)

b)

c)

PM me for a list of exercises.

Note we usually call the discriminant . (Captial Greek letter for D.)

So

ill try those

i sort of understand it now. But.. the question that is starting to really annoy me is:

Find the values of m such that the following quadratic equations have
(i) one root
(ii) two roots

a) x2 -mx + 2 = 0


.. the problem is.. what do you do with the m. It seems to throw me off

 

[SpiralFlex]

i) Remember what was said. When we have one root! We actually have 2 of the same solutions, eg. 8 and 8.

So referring back to what I have said.



Now , ,

So,





ii) Two roots = two different solutions

So what do we use? Yup,



Now , ,





Have you learnt how to solve these inequalities? Draw a parabola! Part above it is,

,

Note: Don't be afraid to try and make mistakes, that's the only way you can learn effectively.

 

[funnytomato]

ill try those

i sort of understand it now. But.. the question that is starting to really annoy me is:

Find the values of m such that the following quadratic equations have
(i) one root
(ii) two roots

a) x2 -mx + 2 = 0


.. the problem is.. what do you do with the m. It seems to throw me off

find the discriminant as an expression involving m
then solve the equation/inequality

 

[SpiralFlex]

Also some questions asked especially in the 2U HSC exam is for which values of are the roots rational/irrational, so learn this before moving ahead.

 

[someth1ng]

ill try those

i sort of understand it now. But.. the question that is starting to really annoy me is:

Find the values of m such that the following quadratic equations have
(i) one root
(ii) two roots

a) x2 -mx + 2 = 0


.. the problem is.. what do you do with the m. It seems to throw me off

Basically, you use the [-b+/-sqrt(b^2-4ac)]/2a

Substitute it all in with m and solve.

ie.

[-b+/-sqrt(b^2-4ac)]/2a=0 for one root

AND

[-b+/-sqrt(b^2-4ac)]/2a>0 for two roots

 

[SpiralFlex]

Let me summarise for you epicFAILx.

So we said before

1. If , the quadratic equation has 2 REAL and UNEQUAL roots!

This note can be divided into two sections,

a. If is also a perfect square, these two roots are RATIONAL!

b. If is not a perfect square, these two roots are IRRATIONAL!


2. If , then the quadratic equation has REAL and EQUAL roots!

3. If , then the quadratic equal has NO REAL roots! [Note: It will have a complex root, which will be delt with in 4 Unit Mathematics.]


Terms

- Real roots: They are just numerical solutions such as -1, 2, 2.1, etc...[So far throughout kindy and Year 11, we have used real numbers. Complex and imaginary numbers are used if you choose to do 4 Unit Mathematics.]

- Unequal roots: 8 and 7 are unequal roots. 6 and 1 are unequal, so on.

- Rational roots: Can be expressed in the form of

- Irrational roots: Cannot be expressed in the form of

- Perfect square: Number that can be square rooted without a decimal answer. [Eg. 64, 100]

Also on occasions you will be asked for what values of has the quadratic have REAL SOLUTIONS.

When,

 

[epicFAILx]

i) Remember what was said. When we have one root! We actually have 2 of the same solutions, eg. 8 and 8.

So referring back to what I have said.



Now , ,

So,





ii) Two roots = two different solutions

So what do we use? Yup,



Now , ,





Have you learnt how to solve these inequalities? Draw a parabola! Part above it is,

,

Note: Don't be afraid to try and make mistakes, that's the only way you can learn effectively.

Oh My Gosh. SO its just simple substitution after finding out about the discriminant case (in this q)?!

 

[SpiralFlex]

Oh My Gosh. SO its just simple substitution after finding out about the discriminant case (in this q)?!

Yes, that's all it is! Then of course you need to understand what you are actually doing. The Cambridge book has superb questions regarding the discriminant in Chapter 8. Go have a try if you have the Cambridge book. Have I confused you? If I have let me know, I can start from scratch if you need to.

 

[4025808]

Oh My Gosh. SO its just simple substitution after finding out about the discriminant case (in this q)?!

Yes, also noting that if you're finding the roots in terms of x, then treat m as a constant like how you would treat numbers as constants

Edit: yay it's my 1100th post