Question

Solving the following quadratic equation by factorization method:

\[x^2 + 10ix - 21 = 0\]

Answer 1

\[ x^2 + 10ix - 21 = 0\]

\[ \Rightarrow x^2 + 7ix + 3ix - 21 = 0\]

\[ \Rightarrow x\left( x + 7i \right) + 3i\left( x + 7i \right) = 0\]

\[ \Rightarrow \left( x + 7i \right)\left( x + 3i \right) = 0\]

\[ \Rightarrow \left( x + 7i \right) = 0 or \left( x + 3i \right) = 0\]

\[ \Rightarrow x = - 7i, - 3i\]

\[\text { So, the roots of the given quadratic equation are - 3i and - 7i } .\]