Question

find the roots of quadratic equation x²+x+2=0 using quadratic formula.

Answer 1

Given Equation is x^2 + x + 2 = 0.

Here a = 1, b = 1, c = 2.

Now, We have to calculate the Discriminant.

D = b^2 - 4ac

⇒ (1)^2 - 4(1)(2)

⇒ 1 - 8

⇒ -7.

The Quadratic formula is :

(i)

$x = \frac{-b + \sqrt{b^2 - 4ac}}{2a}$

$= > \frac{-(1) + \sqrt{-7}}{2}$

$= > \frac{-1 + \sqrt{7} \sqrt{-1}}{2}$

We know that √-1 = i.

$= > \frac{-1 + \sqrt{7} i}{2}$

$= > -\frac{1}{2} + \frac{\sqrt{7}}{2} i$

(ii)

$= > x = \frac{-b - \sqrt{b^2 - 4ac}}{2a}$

$= > \frac{-1 - \sqrt{-7}}{2}$

$= > \frac{-1 - \sqrt{7}i}{2}$

$= > -\frac{1}{2} - \frac{\sqrt{7}}{2}i$

Therefore the roots are,

$= > \boxed{x = -\frac{1}{2} + \frac{\sqrt{7}}{2}i,-\frac{1}{2} - \frac{\sqrt{7}}{2}i}$

Hope this helps!

Answer 2

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Hope it helps!