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If a ,\ b are the roots of the equation ...

If `a ,\ b` are the roots of the equation `x^2+x+1=0,\ then\ a^2+b^2=` 
a)1 b)2 c)-1 d)3

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The correct Answer is:
`a^2+b^2=−1`
Sum of the roots` ⇒a+b=−1 ` ...(1)
Product of the roots` ⇒ab=1 ` ...(2)
We know that,
`(a+b)^2=a^2+b^2+2ab`
`⇒a^2+b^2=(a+b)^2−2ab`
Substituting (1) and (2) in the above equation, we get
`⇒a^2+b^2^2=(−1)^2−2(1)`
`∴a^2+b^2=−1`
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