Find the solutions to x^3+4x^2+x-5=1

MYTUTOR SUBJECT ANSWERS

Answers / Maths / A Level / Find the solutions to x^3+4x^2+x-5=1

552 views

Find the solutions to x^3+4x^2+x-5=1

These cubic equations are usually fairly simple once the method is known, firstly make the right hand side (RHS) equal to zero by subtracting 1 from both sides:

x^3+4x^2+x-6=0

Now the next step is a quick bit of trial and error, one of the roots to this equation is a factor of 6 so this leaves us with ±1, ±2, ±3, ±6. So plug these into the equation until you get a result which equals zero.

After trialling we find that +1 is a root or in factorised form (x-1). This leads us to our next step:

What quadratic multiplied by our factorised root gives us our original equation?

(x-1)(ax^2+bx+c)=x^3+4x^2+x-6

Well the coefficient of x^3 is 1 so our value of 'a' must also be 1 (If the coeffiecient of x^3 was 5 then 'a' would also be 5)

(x-1)(x^2+bx+c)=x^3+4x^2+x-6

The constant term 'c' must equal -6 when multiplied by -1 and so c= (-6/-1) =6

(x-1)(x^2+bx+6)=x^3+4x^2+x-6

Now we need to find b...

The coefficient of x in the problem was 1, so we need to find a value of 'b' so that when the brackets are expanded there is 1x:

1x=bx*(-1)+x*6 so b=5

This gives us:

(x-1)(x^2+5x+6)=x^3+4x^2+x-6

(x-1)(x^2+5x+6)=0

Factorise the quadratic either by inspection or by using the quadratic formula:

(x-1)(x+2)(x+3)=0

so the roots are x=1,-2,-3

Luke H. A Level Maths tutor, GCSE Maths tutor, 11 Plus Maths tutor, 1...

1 year ago

Answered by Luke, an A Level Maths tutor with MyTutor

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

309 SUBJECT SPECIALISTS

Ayyub A. A Level Maths tutor, 13 Plus Maths tutor, 11 Plus Maths tut...

View profile

£24 /hr

Ayyub A.

Degree: Mathematics Msci (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics + 1 more

“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.”

5.0

47 reviews | 50 completed tutorials

Save profile

View profile

£20 /hr

Javed R.

Degree: Biomedical Engineering (Bachelors) - Liverpool University

Subjects offered:Maths, Chemistry

“Postgraduate Biomedical Engineering student at the University of Strathclyde. Past classroom experience.”

5.0

2 reviews | 4 completed tutorials

Save profile

Hinsum W. A Level Chemistry tutor, A Level Biology tutor, GCSE Maths ...

View profile

£24 /hr

Hinsum W.

Degree: Medicine (Bachelors) - Edinburgh University

Subjects offered:Maths, Chemistry+ 3 more

“Hi, I'm a first year medic at Edinburgh. I've had 7 years' worth of experience teaching children Maths and English and have mentored lower school peers, so I'm bound to have an approach that will suit your learning style!”

5.0

84 reviews | 147 completed tutorials

Save profile

See more A Level Maths tutors

About the author

View profile

£20 /hr

Luke H.

Degree: Aerospace Engineering (Masters) - Bristol University

Subjects offered:Maths, Science+ 6 more

“Myself I study Aerospace Engineering at Bristol University, I have a genuine love for sciencebased subjects especially physics and maths, ask me anything you want to know and even if I don't know the answer (we are all human), I will ...”

MyTutor guarantee

Save profile

Version:	3.46.2
Build:	6112849ddb05
Time:	2017-06-27T12:45:38Z

MYTUTOR SUBJECT ANSWERS

Find the solutions to x^3+4x^2+x-5=1

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

309 SUBJECT SPECIALISTS

About the author

You may also like...

Other A Level Maths questions

One-to-one help is at your fingertips