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Question

If a and b are roots of the equation x2-x+1=0, then write the value of a2 + b2.

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Solution

Given: x2 - x + 1 = 0
Also, a and b are the roots of the equation.
Then, sum of the roots = a + b = - -11 = 1

Product of the roots = ab = 11 = 1

a + b2 = a2 + b2 + 2ab 12 = a2 + b2 + 2×1 a2+ b2 = 1 - 2 =-1 a2 + b2 =-1

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