Question

Which of the following expressions is equal to 3x^2+27

Answer 1

Answer:

The roots of the the given equation are +3i or -3i.

Solution:

Given, $3x^2+27=0$

First of all compare the given equation with the standard form, i.e $ax^2+bx+c=0$

On comparing,  

a=3

b=0

c=27

According to the quadratic formula,

$x = \frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$b^2-4ac= 0-4\times3\times27=-324$

As $b^2-4ac$ comes out to be negative, the given equation does not have any real roots,

$\sqrt {b^2-4ac}= \sqrt{(-324)}$

$\sqrt {b^2-4ac}= \sqrt{(324\times -1)}$

$\Rightarrow \sqrt{324}\times \sqrt{-1}$

Root of 324 is 18,

$\Rightarrow 18\times i$ (Because root of -1 is i)

$x=\frac{(-0+-18i)}{2\times3}$

$x=\frac{\pm18i}{6}$

$x=\frac{+18}{6} \ or \frac{-18}{6}$

On dividing 18 and 6 we get,

$\therefore x=+3i \ or -3i$