Question

Find a quadratic equation with roots -1+4i and -1-4i.

Answer 1

Hello,

(x-(-1+4i))(x-(-1-4i))=((x+1)-4i)((x+1+4i)
=((x+1)²+16
=x²+2x+17

Answer 2

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 )

$x^2 + 2x + 17$