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Question

If a, b are the roots of the equation x2+x+1=0, then a2+b2=
(a) 1
(b) 2
(c) −1
(d) 3

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Solution

(c) −1
Given equation: x2 + x + 1 = 0
Also, a and b are the roots of the given equation.
Sum of the roots = a + b =-Coefficient of xCoefficient of x2=- 11 =-1

Product of the roots = ab = Constant term Coefficient of x2 =11= 1

(a + b)2 = a2 + b2 + 2ab (-1)2 = a2 + b2 + 2×1 1 - 2 = a2 + b2 a2 + b2 =-1

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