Joshua F. GCSE Chemistry tutor, GCSE Maths tutor, A Level Maths tutor...

Joshua F.

Currently unavailable: no new students

Degree: Chemical Engineering w/ industrial experience (Masters) - Manchester University

MyTutor guarantee

|  1 completed tutorial

Contact Joshua

About me

Hi, I'm Josh!
I'm a fist year studying Chemical Engineering at Manchester currently and I sometimes get way too excited about mathematics... I enjoyed maths at school, so much so I taught myself an extra module (Mechanics 3) for which i got 90%. 

Besides acadaemic studies I'm a keen muscian, with piano, clarinet and voice up to grade 8, and I also like to keep myself busy playing guitar, saxophone and the organ. I'm a university rower and an avid cyclist, so I understand how difficult it can be to fit homework/coursewokrk around everything else in life! I've recently been awarded the BP STEM Scholarship which was given to only 90 students across the UK.

 

I hope I can make things easy to understand for anyone, and help you to achieve greatness! 

Subjects offered

SubjectQualificationPrices
Maths A Level £20 /hr
Physics A Level £20 /hr
Chemistry GCSE £18 /hr
Maths GCSE £18 /hr
Physics GCSE £18 /hr
Science GCSE £18 /hr

Qualifications

SubjectQualificationLevelGrade
MathematicsA-levelA2A*
PhysicsA-levelA2A*
ChemistryA-levelA2A
Further MathematicsA-levelA2A
Disclosure and Barring Service

CRB/DBS Standard

No

CRB/DBS Enhanced

No

Questions Joshua has answered

How to find the roots of a Quadratic Equation by Factorising?

Suppose you have a quadratic equation: x2 + 5x + 6 You are told it has TWO REAL ROOTS and you are to find them. The factorised quadratic with two roots will look like this: (x+a)(x+b) Where a and b are real numbers (any positive or negative number really) As this is just another form of the ...

Suppose you have a quadratic equation: x+ 5x + 6

You are told it has TWO REAL ROOTS and you are to find them.

The factorised quadratic with two roots will look like this:

(x+a)(x+b)

Where a and b are real numbers (any positive or negative number really)

As this is just another form of the original equation we can say they are equal:

(x+a)(x+b) = x+ 5x + 6

 

If you mulitply out the brackets using the FOIL (First, Outside, Inside, Last) rule you get:

x2 + xa + xb + ab = x+ 5x + 6

It's clear the x2 terms cancel out, and if we equate the x terms and the number terms, we are left with

xa + xb = 5x        and  ab= 6

x(a+b) = 5x                  a x b = 6

a + b = 5

So now we must use this information to find a and b.

The factors of 6 are:

6 and 1 

3 and 2

Of those factors, the pair which adds to 5 are 3 and 2.

so a = 3 and b = 2

Now we must check the signs of the factorised equation to check when we multiply ot the bracket we get the original equation again.... 

(x+3)(x+2) = x2 + 5x + 6 - CORRECT

Now we use this to find the roots, i.e. the x coordinates were y = 0 

so therefore we make our factorised quadratic equal to 0

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

If two things multiplied together = 0, then at least one of them must equal 0...

x+3 = 0 ==> x = -3

OR

x+2 = 0 ==> x = -2

 

We can check the roots are corrects by replacing a and b with the x terms in the original equation and it should equal 0 for both a and b

We now have our roots...

x = -3 

and x = -2

see more

3 years ago

754 views
Send a message

All contact details will be kept confidential.

To give you a few options, we can ask three similar tutors to get in touch. More info.

Contact Joshua

Still comparing tutors?

How do we connect with a tutor?

Where are they based?

How much does tuition cost?

How do tutorials work?

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