Question

If a and b are the zeroes of the polynomial x^2+x+1 then what is the value of 1/a+1/b

Answer 1

a+b=-1

ab=1

1/a+1/b=a+b/ab=-1/1=-1

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Answer 2

For a quadratic equation of the form, ax^2 + bx + c

Sum of the roots. = (-)b/a

Product of the roots = c/ a

So, in the given quadratic equation

The sum of the roots, i.e a+b = (-)1/1

Product of the roots, i.e ab. = 1/1

Now 1/a+ 1/b = a+b/ ab

= (-)1/1

= (-)1

Hope it helps ^_^