Question
Show the following quadratic equation by factorization method:
$x^2 + 4x + 7 = 0$
$x^2 + 4x + 7 = 0$
✓
Answer
$x^2 + 4x + 7 = 0$
We will apply discriminant rule,
$\text{x}=\frac{-\text{b}\pm\sqrt{\text{D}}}{2\text{a}}\ ...(\text{A})$
Where $D = b^2 - 4ac = (-4)^2 - 4.1.7 = -12$
From (A)
$\text{x}=-\frac{(-4)\pm\sqrt{-12}}{2}$
$=\frac{4\pm2\sqrt{3}\text{i}}{2}$
$=2\pm\sqrt{3}\text{i}$
$\therefore\text{x}=2+\sqrt{3}\text{i},2-\sqrt{3}\text{i}$
We will apply discriminant rule,
$\text{x}=\frac{-\text{b}\pm\sqrt{\text{D}}}{2\text{a}}\ ...(\text{A})$
Where $D = b^2 - 4ac = (-4)^2 - 4.1.7 = -12$
From (A)
$\text{x}=-\frac{(-4)\pm\sqrt{-12}}{2}$
$=\frac{4\pm2\sqrt{3}\text{i}}{2}$
$=2\pm\sqrt{3}\text{i}$
$\therefore\text{x}=2+\sqrt{3}\text{i},2-\sqrt{3}\text{i}$
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