Given that for all real values of xxx:
x2+4x>2x−k x^2 + 4x > 2x - k x2+4x>2x−kfind the range of possible values of kkk.
"If I add 2 to a number and then square the sum, the result is greater than the square of the original number."
Find the range of values of the number for which the above statement is true.
257 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof. Each one has a worked solution and a mark scheme showing where the marks go.