For the following equation under the given condition a find

For the following equation under the given condition, (a) find k, and (b) find a second solution. x^2 - kx + 41 = 0; one solution is 4 + 5i (a) k = (Type an integer or a simplified fraction.) (b) A second solution is x = (Type your answer in the form a + bi.)

Solution

x²-kx+41=0

given 4+5i is the solution

for the quadratic equation with real coefficients if a+ib is the solution then its conjugate a-ib is also the solution

so the second solution is 4-5i

sum of roots =-k

-k =(4+5i)+(4-5i)

-k=8

=>k =-8

k=-8, second solution is 4-5i