You are Here: Home >< Maths

2x^2+(3-K)x+K+3=0 Maths help? Watch

Announcements
1. I have to find the range of values K could have for 2x^2+(3-K)x+K+3=0 to have two real distinct roots. If someone understands this, please help out!
2. (Original post by ~xSarahx~)
I have to find the range of values K could have for 2x^2+(3-K)x+K+3=0 to have two real distinct roots. If someone understands this, please help out!
for the quadratic to have two distinct roots
3. (Original post by DylanJ42)
for the quadratic to have two distinct roots
Thanks! I understand that but I just honestly don't understand how to figure this whole thing out :/ I can't really find any good examples online and it's just really confusing me.
4. (Original post by ~xSarahx~)
Thanks! I understand that but I just honestly don't understand how to figure this whole thing out :/ I can't really find any good examples online and it's just really confusing me.
In your quadratic what do you think a=, b= and c= ?

Posted from TSR Mobile
5. (Original post by ~xSarahx~)
Thanks! I understand that but I just honestly don't understand how to figure this whole thing out :/ I can't really find any good examples online and it's just really confusing me.
do you understand the quadratic formula, or at least how it gets you the roots of a quadratic?

well the quadratic formula tells us that the roots of the quadratic equation are

As you know you cannot square root a negative number so in order for real roots to exist the part under the square root sign must be > 0.

If the part under the square root is zero we end up with which means both roots are the same. You still get 2 roots but they are same ie not distinct roots.

Finally if the part under the sqaure root is positive then you get two distinct roots, namely and

In Summary;

So if a quadratic has no real roots then the part under the square root sign is negative ie

If a quadratic has a repeated root (this means both x values you find from the quadratic formula are the same) then the part under the square root sign is equal to 0 ie

Finally if a quadratic has two distinct roots then the part under the square root is > 0 ie

I hope this clears it up at least a little for you
6. (Original post by gdunne42)
In your quadratic what do you think a=, b= and c= ?

Posted from TSR Mobile
That's another issue I'm having.
so
a= 2xˆ2

but I'm not sure where that x between (3-k) and k+3 goes.

is it
b= (3-k)x OR b=(3-k)

c=k+3 OR c=x+K+3

I've never done this with k before which is why i'm so useless at this...
7. (Original post by DylanJ42)
do you understand the quadratic formula, or at least how it gets you the roots of a quadratic?

well the quadratic formula tells us that the roots of the quadratic equation are

As you know you cannot square root a negative number so in order for real roots to exist the part under the square root sign must be > 0.

If the part under the square root is zero we end up with which means both roots are the same. You still get 2 roots but they are same ie not distinct roots.

Finally if the part under the sqaure root is positive then you get two distinct roots, namely and

In Summary;

So if a quadratic has no real roots then the part under the square root sign is negative ie

If a quadratic has a repeated root (this means both x values you find from the quadratic formula are the same) then the part under the square root sign is equal to 0 ie

Finally if a quadratic has two distinct roots then the part under the square root is > 0 ie

I hope this clears it up at least a little for you
Thank you for explaining it out like that! The question is starting to make more sense for me!
8. Perhaps this way will make it clearer.

For the equation (a)x^2 + (b)x + (c) = 0, we want b^2-4ac > 0.

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

Perhaps looking at it that way will make it a little easier to understand.
9. (Original post by ~xSarahx~)
That's another issue I'm having.
so
a= 2xˆ2

but I'm not sure where that x between (3-k) and k+3 goes.

is it
b= (3-k)x OR b=(3-k)

c=k+3 OR c=x+K+3

I've never done this with k before which is why i'm so useless at this...

a is the coefficient of the x^2 term = 2
b is the coefficient of the x term = (3-k)
c is the constant at the end = (k+3)

Posted from TSR Mobile
10. (Original post by ~xSarahx~)
Thank you for explaining it out like that! The question is starting to make more sense for me!
youll get by if you learn off the summary part at the bottom. Just know whether to use , , depending on whether they ask for 2 distinct roots, 1 repeated root or 0 real roots
11. (Original post by sammygmfc)
Perhaps this way will make it clearer.

For the equation (a)x^2 + (b)x + (c) = 0, we want b^2-4ac > 0.

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

Perhaps looking at it that way will make it a little easier to understand.
Oh oh ohhhh!

So...perhaps

(3-k)ˆ2 - (4x2x[k+3]) > 0 would be..right? Or am I still not getting it?
12. (Original post by ~xSarahx~)
Oh oh ohhhh!

So...perhaps

(3-k)ˆ2 - (4x2x[k+3]) > 0 would be..right? Or am I still not getting it?
That's it

Posted from TSR Mobile
13. (Original post by ~xSarahx~)
Oh oh ohhhh!

So...perhaps

(3-k)ˆ2 - (4x2x[k+3]) > 0 would be..right? Or am I still not getting it?
That's right. Then solve to find the set of values for which k could be.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 3, 2016
Today on TSR

Oxbridge

Even more elitist than everyone thought?

Physically ill after being cheated on

Discussions on TSR

• Latest
• See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants

Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.