Solve the quadratic equations by factorization method only 21x2 + 9x + 1 = 0

Given: 21x² + 9x + 1 = 0

We shall apply discriminant rule,

Where, \(x= \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\)

Here, a = 21, b = 9, c = 1

So,

\( x=\dfrac{(-9 ±\sqrt{(9^2 – 4 (21)(1)))}}{2(21)}\)

= \( \dfrac{ (-9 ± \sqrt{3(-1))}}{42}\)

We have i² = –1

By substituting –1 = i² in the above equation, we get

\( x=\dfrac{(-9 ± \sqrt{3i^2)}}{42}\)

= \( -\dfrac{3}{14}±\sqrt{\dfrac{3i}{42}}\)

The roots of the given equation are \( -\dfrac{3}{14}±\sqrt{\dfrac{3i}{42}}\)