MYTUTOR SUBJECT ANSWERS

205 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...

8 months ago

Answered by Luke, an A Level Maths tutor with MyTutor

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

182 SUBJECT SPECIALISTS

£30 /hr

Fahad M.

Degree: Medicine And Surgery - MBChB (Bachelors) - Birmingham University

Subjects offered: Maths, Psychology+ 7 more

Maths
Psychology
Physics
Chemistry
Biology
.UKCAT.
.BMAT (BioMedical Admissions)
-Personal Statements-
-Medical School Preparation-

“About MeGraduating highschool with many distinctions I went on to become a medical student at the University of Birmingham. Having excelled in my interview (gaining the top rank in Motivation and Experience) I went on immediately to ...”

£22 /hr

Hayden M.

Degree: Physics (Masters) - Warwick University

Subjects offered: Maths, Science+ 4 more

Maths
Science
Physics
Further Mathematics
English
Chemistry

“My name is Hayden. I am a 2nd year Physics student at The University of Warwick. I get excited aboutall things science and I hope that I can help you not only learn your material but alsounderstand why it is a useful thing to know.A...”

£20 /hr

Jasmine S.

Degree: Mathematics (Bachelors) - Exeter University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hi, I'm Jasmine and I'm a second year Mathematician at Exeter University, I'm looking to help students prepare for their Maths and Physics exams.”

About the author

£20 /hr

Luke H.

Degree: Aerospace Engineering (Masters) - Bristol University

Subjects offered: Maths, Science+ 6 more

Maths
Science
Physics
English
Design & Technology
Chemistry
Biology
-Personal Statements-

“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

You may also like...

Other A Level Maths questions

Given that y = exp(2x) * (x^2 +1)^(5/2), what is dy/dx when x is 0?

The curve C has equation y = x^3 - 2x^2 - x + 9, x > 0. The point P has coordinates (2, 7). Show that P lies on C.

Find the tangent to the curve y=x^3+3 at the point x=1.

The variable x=t^2 and the variable y=2t. What is dy/dx in terms of t?

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok