Question

What would be the root of (x^2 + 2)?

Answer 1

Answer:

The roots of the equation are $\sqrt{2}i$ and  $-\sqrt{2}i$

Step-by-step explanation:

The roots of a quadratic equation y = ax² + bx + c are the values of x at y = 0

∵ y = x² + 2

- To find the roots of it equate y by 0

∴ 0 = x² + 2

- Switch the two sides

∴ x² + 2 = 0

- Subtract 2 from both sides

∴ x² = -2

- Take √  for both sides

∴ x = ± $\sqrt{-2}$

- There is no square root for negative numbers

∴ There is no real roots for this equation but there are imaginary roots

∵ $\sqrt{-1}=i$

∴ $\sqrt{-2}=\sqrt{2}*\sqrt{-1}$

- Substitute $\sqrt{-1}$ by $i$

∴  $\sqrt{-2}=\sqrt{2}*i$

∴  $\sqrt{-2}=\sqrt{2}i$

∴ The roots of the equation are $\sqrt{2}i$ and  $-\sqrt{2}i$