Year 12s: what will be the first way you research your future options? >>

Algebra Inequality

Taken from an IB algebra worksheet:

Find the range of values of m such that for all x
m(x+1) ≤ x²

It looks misleadingly simple, but I'm not sure...roots of unity came to mind with the x² being there but just an idea.

Any help appreciated

Reply 1

SimonM

What can you tell me about quadratics and their roots?

Spoiler

Reply 2

Oh I Really Don't Care

0 < x^2 - m(x+1) = x^2 - mx - m = (x - \frac{m}{2})^2 - m - \frac{m^2}{4}

easier now? [critical values]

Reply 3

IBiot Ash '08

Do you mean that x² has to be positive?

Reply 4

Oh I Really Don't Care

Maybe consider the simon's hint or consider other values.

Reply 5

IBiot Ash '08

DeanK22

0 < x^2 - m(x+1) = x^2 - mx - m = (x - \frac{m}{2})^2 - m - \frac{m^2}{4}

easier now? [critical values]

could i not just look at the discriminant from there? i.e. where it is less than equal to zero

Reply 6

azhao

Just consider the critical values and use the table method
.

Reply 7

Oh I Really Don't Care

IBiot Ash '08

could i not just look at the discriminant from there? i.e. where it is less than equal to zero

CTS is just something I would do. You at liberty to use the discriminant if you please.

Reply 8

IBiot Ash '08

azhao

Just consider the critical values and use the table method
.

You lost me...I don't think I've done this yet, and even if i have it's after 10pm..I apologise for being particularly braindead....

Reply 9

SimonM

IBiot Ash '08

You lost me...I don't think I've done this yet, and even if i have it's after 10pm..I apologise for being particularly braindead....

Use the discriminant. If it* is always positive, how many roots does it have?

*x^2-mx-m

Reply 10

IBiot Ash '08

SimonM

Use the discriminant. If it* is always positive, how many roots does it have?

*x^2-mx-m

2..But I can't see how that helps

Reply 11

SimonM

IBiot Ash '08

2..But I can't see how that helps

Its always nonnegative

Edit: positive -> nonnegative

Latest

Articles for you

Clearing 2024: how to call universities

Best places online for maths revision

What is an LLM and how could it benefit your career?

Powerful questions business students forget to ask their career advisers

Algebra Inequality

Related discussions

Latest

Trending

Trending

Articles for you