
06312022
j
2014d.00672
Miles, David
A hornet's nest.
Math. Sch. (Leicester) 43, No. 1, 17 (2014).
2014
Mathematical Association (MA), Leicester
EN
H34
quadratic equations
nested surds
simplification
completed square
discriminant
perfect square
solving equations
manipulation of expressions
From the text: I set my year 12 further mathematicians a deceptively simple question as a starter. Prove $1+\sqrt{3}$ is a solution of the quadratic equation $x^24x+2\sqrt{3}=0$ and hence, or otherwise, find the other solution in its simplest exact form. The first part presented no difficulty, but I was a little disappointed that no one spotted the efficient way to tackle the second part.