Question

Solve the following quadratic equation by factorisation.

 x² – 15x + 54 = 0

Answer 1

x² – 15x + 54 = 0 

\[\Rightarrow x^2 - 9x - 6x + 54 = 0\]
\[ \Rightarrow x\left( x - 9 \right) - 6\left( x - 9 \right) = 0\]
\[ \Rightarrow \left( x - 6 \right)\left( x - 9 \right) = 0\]
\[ \Rightarrow \left( x - 6 \right) = 0 \text{ or } \left( x - 9 \right) = 0\]
\[ \Rightarrow x = 6  \text{ or }  x = 9\] 

So, 6 and 9 are the roots of the given quadratic equation.