Top answers

Show that if a polynomial with integer coefficients has a rational root, then the rational root must be an integer. Hence, show that x^n-5x+7=0 has no rational roots.

Let f(x)=x^n+a_(n-1)x^(n-1)+...+a_0 with n>=2 and a_i an integer have a rational root x=p/q. Consider q^(n-1)f(p/q). q^(n-1)f(p/q)=p^n/q+a_(n-1)p^(n-1)+...+a_0q^(n-1)=0 ==> a_(n-1)p^(n-1)+...+a_0q^(n-1...
PA
Answered by Peter A. • STEP tutor
5969 Views

How to differentiate tan(x)?

tanx = sinx/cosx. Express this as: sinx*(cosx)^-1. Remembering the product rule: "y = f(x)g(x), dy/dx = f'(x)g(x) + f(x)g'(x)". sinx differentiates to cosx and cosx differentiates to -sinx. Also, r...
KA
Answered by Kai A. • Maths tutor
12964 Views

How do I tackle the personal statement?

Writing a personal statement for any course is a daunting task and when the course you're applying for has a 10 people applying for every 1 place, it can at times seem impossible. As a current medical studen...
JM
2750 Views

What is the geometry of a ClF3 molecule? (AQA Unit 1 2015 1d)

Chlorine, Cl, and Florine, F are both in group 7 of the periodic table so they have 7 electrons in the outer energy level, called valence electrons. Each fluorine atom makes one covalent bond to the chlorine...
EC
Answered by Eleanor C. • Chemistry tutor
15589 Views

How to complete the square?

This is a handy trick for quadratic equations ax^2 + bx + c = 0. e.g. (x^2 + 5x + 6). So a = 1, b = 5 and c = 6. To complete the square, let x^2 + 5x + 6 = 0. Then, take 6 to the other side to get x^2 + 5x =...
JP
Answered by Jigar P. • Maths tutor
5184 Views