Show the following quadratic equation by factorization method: 21… - Vidyadip

Question

Show the following quadratic equation by factorization method:
21x² + 9x + 1 = 0

✓

Answer

21x² + 9x + 1 = 0
Comparing the given equation with the general form
ax² + bx + c = 0, we get a = 21, b = 9, c = 1
Substituting a and b in,
$\alpha=\frac{-\text{b}+\sqrt{\text{b}^2-4\text{ac}}}{2\text{a}}$ and $\beta=\frac{-\text{b}-\sqrt{\text{b}^2-4\text{ac}}}{2\text{a}}$
$\alpha=\frac{-9+\sqrt{81+84}}{42}$ and $\beta=\frac{-9-\sqrt{81-84}}{42}$
$\Rightarrow\alpha=\frac{-9+\sqrt{-3}}{42}$ and $\beta=\frac{-9-\sqrt{-3}}{42}$
$\Rightarrow\alpha=\frac{-9+\text{i}\sqrt{3}}{42}$ and $\beta=\frac{-9-\text{i}\sqrt{3}}{42}$
The roots are $\text{x}=\frac{-9}{42}\pm\frac{\text{i}\sqrt{3}}{42}$

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