Question

Quadratic equation whose roots are 3+2i and 3-2i.......where i2=-1

Answer 1

two roots are 3+2i and 3-2i

let the quadratic equation be x2- Sx+P

where S is sum of roots and P is product of roots

sum of roots = 3+2i+3-2i

= 6

S = 6

product of roots = (3-2i)(3-2i)

9-(2i)^2. [(a+b)(a-b) = a2-b2]

= 9-4i2

9-4(-1) [i2= -1]

= 9+4= 13

P= 13

put the value of S and P in assumed equation

x2-6x+13

so this is the required equation

Answer 2

Answer:

Step-by-step explanation:

two roots are 3+2i and 3-2i

let the quadratic equation be x2- Sx+P

where S is sum of roots and P is product of roots

sum of roots = 3+2i+3-2i

= 6

S = 6

product of roots = (3-2i)(3-2i)

9-(2i)^2. [(a+b)(a-b) = a2-b2]

= 9-4i2

9-4(-1) [i2= -1]

= 9+4= 13

P= 13

put the value of S and P in assumed equation

x2-6x+13

so this is the required equation