Question

find a cubic equation with real coefficients two of whose roots are 1 and 3+2iota​

Answer 1

Answer:

x³-7x²+19x-13

Step-by-step explanation:

Since one root is 3 + 2i therefore other will be 3-2i as Imaginary roots are in pairs.

Sum of roots = 7

Product of roots = (3+2i)(3-2i)= 9 -4i² = 9+4 = 13

Product of roots taken two at a time = (3 + 2i)×1 +(3-2i)×1

+(3+2i)(3-2i) = 6 + 13 = 19

Therefore the equation will be

x³ - sum of roots x² + product of roots taken two at a time x - product of roots

= x³-7x²+19x-13