# Using quadratic eq solve x 2-12x+40=0?

Jun 8, 2018

$x = 6 + 2 i$ and $6 - 2 i$

#### Explanation:

As per the question, we have

${x}^{2} - 12 x + 40 = 0$

$\therefore$ By applying the quadratic formula, we get

x = (-b±sqrt(b^2-4ac))/(2a)

:.x = (-(-12)±sqrt((-12)^2-4(1)(40)))/(2(1))

:.x = (12±sqrt(144-160))/2

:.x =(12±sqrt(-16))/2

Now, as our Discriminant ( $\sqrt{D}$ ) $< 0$, we're gonna get imaginary roots (in terms of $i$ / iota).

:.x=(12±sqrt(16)xxsqrt(-1))/2

:.x=(12±4 xx i)/2

:.x=(6±2i)

$\therefore x = 6 + 2 i , 6 - 2 i$

Note : For those who don't know, $i$ ( iota ) = $\sqrt{- 1}$.