Answer:
The roots of the equation are [tex]\sqrt{2}i[/tex] and [tex]-\sqrt{2}i[/tex]
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 = ± [tex]\sqrt{-2}[/tex]
- There is no square root for negative numbers
∴ There is no real roots for this equation but there are imaginary roots
∵ [tex]\sqrt{-1}=i[/tex]
∴ [tex]\sqrt{-2}=\sqrt{2}*\sqrt{-1}[/tex]
- Substitute [tex]\sqrt{-1}[/tex] by [tex]i[/tex]
∴ [tex]\sqrt{-2}=\sqrt{2}*i[/tex]
∴ [tex]\sqrt{-2}=\sqrt{2}i[/tex]
∴ The roots of the equation are [tex]\sqrt{2}i[/tex] and [tex]-\sqrt{2}i[/tex]
