When is the inequality x^4 < 8x^2 + 9 true?

If we consider this like a normal quadratic problem, this becomes easy

x4 < 8x2 + 9

x4 - 8x2 - 9 < 0

(x2-9)(x2+1) < 0

This means there are roots of this expression at x2 = 9 and x2 = -1

Since for all reals, x2 > 0, we know the two roots of this expression are x=+-3

Now, since x4 - 8x2 - 9 is a quartic (ie, it has an x4 expression), we know that given any sufficiently positive or negative x, the quartic will be positive (ie, if x is 10000, or -10000)

Therefore, we know for this to be true, -3

Jesse P. A Level Maths tutor, A Level Further Mathematics  tutor, GCS...

2 years ago

Answered by Jesse, an Uni Admissions Test .MAT. tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£30 /hr

Kyle R.

Degree: Mathematics (Masters) - Oxford, Corpus Christi College University

Subjects offered:.MAT., Maths+ 2 more

Further Mathematics

“Hi! I'm Kyle, a 2nd year Oxford undergraduate studying Maths at Corpus Christi College. I aim to be an understanding and friendly face, whilst being thorough with the material I cover. I've acheived A* grades in Maths, Further Maths a...”

£26 /hr

Ayyub A.

Degree: Mathematics Msci (Bachelors) - Bristol University

Subjects offered:.MAT., Maths+ 1 more

Further Mathematics

“Hi I'm Ayyub, current student at Bristol university studying Maths. I have significant tutoring experience in maths and hopefully i'll be able to help you out.”

£25 /hr

Luke B.

Degree: Mathematics (Masters) - Sheffield University

Subjects offered:.MAT., Maths+ 3 more

Further Mathematics
-Personal Statements-

“I am a fun, engaging and qualified tutor. I'd love to help you with whatever you need, giving you the support you need to be the best you can be!”

About the author

Jesse P.

Currently unavailable: until 01/11/2015

Degree: Mathematics (Masters) - Oxford, New College University

Subjects offered:.MAT., Maths+ 1 more

Further Mathematics

“About Me I'm a first year maths student at New College in Oxford. Maths has always felt like a game, rather than a subject to me, and I really hope I can show why, and get you to feel that way.  As well as the online tutoring, I tuto...”

MyTutor guarantee

You may also like...

Posts by Jesse

A table has diameter 130cm. What is the area, as a multiple of Pi

How does the product rule for differentiation work

When is the inequality x^4 < 8x^2 + 9 true?

Why does e^ix = cos(x) + isin(x)

Other Uni Admissions Test .MAT. questions

The sequence xn is given by the formula x_n = n^3 − 9n^2 + 631. What is the largest value of n for which x_n > x_(n+1)?

When is the inequality x^4 < 8x^2 + 9 true?

The inequality x^4 < 8x^2 + 9 is satisfied precisely when...

Circle the correct letter: The equation x^3 - 30x^2 + 108x - 104 = 0 has a) No real roots; b) Exactly one real root; c) Three distinct real roots; d) A repeated root.

View Uni Admissions Test .MAT. tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss