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