Question

Good evening ❤♥❤☺☺

here is your question :-

✨ solve the given quality equation by factorization method-

➡ x²+x+1=0​

Answer 1

x^2+x+1=0

This equation has no real roots.

i.e. it has no real solutions

Proof:

D= b^2-4ac

= 1^2-4×1×1

= 1-4

=-3

Here

D<0

So, given equation has no real roots.

Hence, it can't be solved by factorisation method.

Solution by Quadratic formula-

x= -b+√D/2a or x= -b-√D/2a

= -1+√-3 /2×1. or x= -1-√-3 /2×1

= -1+√-3/2 or = -1-√-3/2

Hence

x= -1+√-3/2 or -1-√-3/2

Answer 2

$\mathbb\red{Your\:Solution}$

$= b {}^{2} - 4ac = (1) {}^{2} - 4(1)(1)$

$= 1 - 4 = - 3 < 0$

$= 3( - 1)$

$= 3i {}^{2}$

$No\:Real\:Roots$

$Then\:$

$x = \frac{ - b + \sqrt{ } }{2a} = {x}^{1} = \frac{ - 1 + \sqrt{3i {}^{2} } }{2} = - \frac{1}{2} + i \frac{ \sqrt{3} }{2}$

$= {x}^{2} = \frac{ - 1 - \sqrt{3i {}^{2} } } {2} = - \frac{1}{2} - i \frac{ \sqrt{3} }{2}$

$\mathbb\Green{Hope\:It\:Helps}$