Question

Which of the following equations is quadratic? x(x2 + 1) = 0 5(4x + 2) = 3 (x + 3)(x + 4) = 5

Answer 1

An equation is quadratic if the highest power of the variable in it is 2.

$1. \\ x(x^2+1)=0 \\ x^3+x=0 \\ \hbox{the highest power: 3} \\ \hbox{not quadratic} \\ \\ 2. \\ 5(4x+2)=3 \\ 20x+10=3 \\ 20x+7=0 \\ \hbox{the highest power: 1} \\ \hbox{not quadratic} \\ \\ 3. \\ (x+3)(x+4)=5 \\ x^2+4x+3x+12=5 \\ x^2+7x+7=0 \\ \hbox{the highest power: 2} \\ \hbox{quadratic}$

(x+3)(x+4)=5 is a quadratic equation.