Question

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

Answer 1

The roots of the equation are
`√(2)i` and
`-√(2)i`

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 = ±
`√(-2)`

- There is no square root for negative numbers

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

∵
`√(-1)=i`

∴
`√(-2)=√(2)*√(-1)`

- Substitute
`√(-1)` by
`i`

∴
`√(-2)=√(2)*i`

∴
`√(-2)=√(2)i`

∴ The roots of the equation are
`√(2)i` and
`-√(2)i`