# Find the possible values of k for the quadratic equation 2kx^2 + 5kx + 5k - 3 =0

Watch
Announcements

Page 1 of 1

Go to first unread

Skip to page:

Find the possible values of k for the quadratic equation 2kx^2 + 5kx + 5k - 3 =0 to have real roots.

so isn't the discriminant supposed to be b^2 -4ac >=0 over here?

but in the ms they just used greater than (>0) sign why?

and why is the curve a sad face? isn't it supposed to be a happy face because the coefficient of x^2 is positive?

so isn't the discriminant supposed to be b^2 -4ac >=0 over here?

but in the ms they just used greater than (>0) sign why?

and why is the curve a sad face? isn't it supposed to be a happy face because the coefficient of x^2 is positive?

Last edited by Aleksander Krol; 1 month ago

0

reply

Report

#2

Hi there,

It's because if it is =0 it would have one "real root" while your question says "real roots" that's plural which means it must be >0

Hope this helps!

It's because if it is =0 it would have one "real root" while your question says "real roots" that's plural which means it must be >0

Hope this helps!

0

reply

(Original post by

Hi there,

It's because if it is =0 it would have one "real root" while your question says "real roots" that's plural which means it must be >0

Hope this helps!

**Apad121**)Hi there,

It's because if it is =0 it would have one "real root" while your question says "real roots" that's plural which means it must be >0

Hope this helps!

0

reply

Report

#4

They
They are plotting to find the value of K. This is no longer the original equation they're plotting but the one beginning -15k² so it is a "sad" face. This is a standard method of finding quadratic inequalities.

(Original post by

oh thanks i inderstood the first part now. but then i don't get why is the curve a sad face though?

**Aleksander Krol**)oh thanks i inderstood the first part now. but then i don't get why is the curve a sad face though?

1

reply

Report

#5

That solution is written very poorly and yes I'd read the question to mean at least one real root. They shouldn't turn the inequality to an equality like that. Instead you read the solution set to the inequality from the sketch (looking at where the curve lies above or on the x-axis) with the intersections 0 and 5/8 in mind.

Bear in mind the sketch is of 3k(-5k + 8) and not the original quadratic. The leading term is -15k^2 hence the "sad face" shape.

Bear in mind the sketch is of 3k(-5k + 8) and not the original quadratic. The leading term is -15k^2 hence the "sad face" shape.

Last edited by _gcx; 1 month ago

1

reply

(Original post by

That solution is written very poorly and yes I'd read the question to mean at least one real root. They shouldn't turn the inequality to an equality like that. Instead you read the solution set from the sketch (looking at where the curve lies above or on the x-axis) with the intersections 0 and 5/8 in mind.

Bear in mind the sketch is of 3k(-5k + 8) and not the original quadratic. The leading term is -15k^2 hence the "sad face" shape.

**_gcx**)That solution is written very poorly and yes I'd read the question to mean at least one real root. They shouldn't turn the inequality to an equality like that. Instead you read the solution set from the sketch (looking at where the curve lies above or on the x-axis) with the intersections 0 and 5/8 in mind.

Bear in mind the sketch is of 3k(-5k + 8) and not the original quadratic. The leading term is -15k^2 hence the "sad face" shape.

0

reply

(Original post by

They

They are plotting to find the value of K. This is no longer the original equation they're plotting but the one beginning -15k² so it is a "sad" face. This is a standard method of finding quadratic inequalities.

**Apad121**)They

They are plotting to find the value of K. This is no longer the original equation they're plotting but the one beginning -15k² so it is a "sad" face. This is a standard method of finding quadratic inequalities.

**Apad121**)

Hi there,

It's because if it is =0 it would have one "real root" while your question says "real roots" that's plural which means it must be >0

Hope this helps!

Last edited by Aleksander Krol; 1 month ago

0

reply

Report

#8

(Original post by

so according to the question the discriminant is >=0 right?

**Aleksander Krol**)so according to the question the discriminant is >=0 right?

0

reply

(Original post by

I would say so, it's not very clear. An actual exam question would be clearer.

**_gcx**)I would say so, it's not very clear. An actual exam question would be clearer.

0

reply

Report

#10

(Original post by

wait,.... over here you said, "It's because if it is =0 it would have one "real root" while your question says "real roots" that's plural which means it must be >0" but when the discriminamt =0 it has 2 repeated real roots so it's still plural though.

**Aleksander Krol**)wait,.... over here you said, "It's because if it is =0 it would have one "real root" while your question says "real roots" that's plural which means it must be >0" but when the discriminamt =0 it has 2 repeated real roots so it's still plural though.

One root is another way of saying repeating root because it only touches the X axis at one point. It isn't called "2 repeated roots" _formally but just "1 repeated root" so it shouldn't be plural.

0

reply

Report

#11

(Original post by

It is standard in A level questions to be worded like this which can be frustrating.

One root is another way of saying repeating root because it only touches the X axis at one point. It isn't called "2 repeated roots" _formally but just "1 repeated root" so it shouldn't be plural.

**Apad121**)It is standard in A level questions to be worded like this which can be frustrating.

One root is another way of saying repeating root because it only touches the X axis at one point. It isn't called "2 repeated roots" _formally but just "1 repeated root" so it shouldn't be plural.

If it was ambiguous, they would/should accept both interpretations.

Last edited by _gcx; 1 month ago

0

reply

Report

#12

Agree with the above, but its always worth checking before you (the book) starts talking about a quadratic discriminant, that

a = 2k

(a is the x^2 coefficient) is not zero. Otherwise the quadratic formula is irrelevant (no quadratic term or divide by zero) and hence the discriminant is irrelevant as well. If you simply assume the discriminant / quadratic formula is valid, you might get into problems. In this case, if k=0 you have

-3 = 0

Its not even valid, never mind having any type of roots.

a = 2k

(a is the x^2 coefficient) is not zero. Otherwise the quadratic formula is irrelevant (no quadratic term or divide by zero) and hence the discriminant is irrelevant as well. If you simply assume the discriminant / quadratic formula is valid, you might get into problems. In this case, if k=0 you have

-3 = 0

Its not even valid, never mind having any type of roots.

Last edited by mqb2766; 1 month ago

0

reply

X

Page 1 of 1

Go to first unread

Skip to page:

### Quick Reply

Back

to top

to top