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Question

Solve the following quadratic equation by factorization method only x2+2x+5=0

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Solution

We have, x2+2x+5=0

x2+2x+(1+4)=0

(x2+2x+1)+4=0

(x+1)24(1)=0

[a2+2ab+b2=(a+b)2]

(x+1)2(4i2)=0[i2=1]

(x+1)2(4i2)=0

(x+1)2(2i)2=0

(x+12i)(x+1+2i)=0

[a2b2=(ab)(a+b)]

(x+12i)=0or(x+1+2i)=0

x=1+2iorx=12i

Hence, the roots are 1+2iand12i.


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