Question

the quadratic equation whose root are (2+i) and (2-i) is

Answer 1

Step-by-step explanation:

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x4−6x3+14x2−22x+5=0

Roots are 2+3,2−3,1+2i,1−2i

Quadratic euation of roots 2+3,2−3 is 

Sum of the roots= (2+3)+(2−3)=4

Product of the roots= (2+3)∗(2−3)=4−3=1

thus,quadratic equation is,

x2−(sum of the roots)x+(product of the roots)=0

i.e, x2−4x+1=0

Quadratic euation of roots 1+2i,1−2i is 

Sum of the roots= (1+2i)+(1−2i)=2

Product of the roots= (1+2i)(1−2i)=1−(2i)2=1−4i