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