MYTUTOR SUBJECT ANSWERS

690 views

Solve x^2-5*x+6=0

There are 2 methods we can use here.

Method 1 - Factorisation

If we can rewrite the equation so that it looks like (x+a)*(x+b)=0, where 'a' and 'b' are numbers, then we can easily find a solution. If one or both of the terms inside the brackets equals 0, then their product is also 0. This means the solution(s) are the values of x such that x+a=0 or x+b=0.

Multiplying out the brackets of (x+a)*(x+b)=0 gives x2+(a+b)*x+a*b=0. If we match up the terms with the equation we want to solve (called comparing coefficients), we see that we want two numbers 'a' and 'b' so that a+b=-5, and a*b=6. The two numbers which satisfy this are -2 and -3, so these are our values for 'a' and 'b'.

Now we can write our equation as (x-2)(x-3)=0 (you can check yourself this can be multiplied out to give the original equation!)

If x-3=0 then x=3, and if x-2=0 then x=2, so these are our two solutions.

Method 2 - Quadratic Formula

This method can be used when you can't easily 'see' the numbers to use to factorise the equation.

The quadratic formula states that for an equation of the form a*x2+b*x+c=0, where 'a', 'b', and 'c' are numbers, then

x=(-b+-sqrt(b2-4*a*c)/(2*a)

For our equation a=1, b=-5 and c=6, which can then be substituted into the formula. Again you can check yourself that it simplifies to give the same answers as method 1

Hannah D. A Level Maths tutor, GCSE Maths tutor, A Level Further Math...

1 year ago

Answered by Hannah, a GCSE Maths tutor with MyTutor


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

630 SUBJECT SPECIALISTS

£18 /hr

Ryan A.

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
.STEP.

“Passionate about passing down a greater understanding of maths and instilling confidence in all students.”

MyTutor guarantee

£24 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

£18 /hr

Tamara A.

Degree: Medicine (Bachelors) - Liverpool University

Subjects offered:Maths, Chemistry+ 1 more

Maths
Chemistry
Biology

“I'm a friendly second year medical student with a year's experience in tutoring. I'm passionate about science, and I'm patient and approachable.”

MyTutor guarantee

About the author

Hannah D.

Currently unavailable: for regular students

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“A bit about me: Hi, I'm Hannah and I have just received my Masters degree in Maths at Bristol University, graduating with a first. I have been a high achiever throughout my time in education and I now hope to help the next generation ...”

MyTutor guarantee

|  2 completed tutorials

You may also like...

Posts by Hannah

How would you differentiate ln(sin(3x))?

Solve x^2-5*x+6=0

Other GCSE Maths questions

Find the solutions of the equation x^2 - 2x - 8 =0

How do you use Pythagoras' Theorem?

How do I know the best way to solve a quadratic equation?

In triangle ABC, right angled at B, AB = 3 cm and AC = 6 cm. Determine angle BAC and angle ACB.

View GCSE Maths 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

mtw:mercury1:status:ok