Answer:
[tex]x^2 + 2x + 17[/tex]
Step-by-step explanation:
Since, a quadratic equation having roots [tex]\alpha[/tex] and [tex]\beta[/tex] is,
[tex]x^2 - (\alpha+\beta)x + \alpha.\beta[/tex]
Here,
[tex]\alpha = -1 + 4i[/tex]
[tex]\beta = -1 - 4i[/tex]
Hence, the required quadratic equation,
[tex]x^2 - (-1+4i- 1 - 4i)x + (-1+4i)(-1-4i)[/tex]
[tex]x^2 + 2x + ( (-1)^2 - (4i)^2)[/tex] ( ∵ a² - b² = (a+b)(a-b) )
[tex]x^2 + 2x + (1 + 16)[/tex] ( ∵ i² = -1 )
[tex]x^2 + 2x + 17[/tex]
