If α and β are the zeros of the polynomial f(x) = x² + x + 1, find the value of 1/α + 1/β

Video Explanation

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Given

f(x) = x² + x + 1

α and β are the zeros of the polynomial.

To Find

The value of 1/α + 1/β.

Solution

For a quadratic polynomial ax² + bx + c:

Sum of zeros, α + β = −b/a
Product of zeros, αβ = c/a

Comparing f(x) = x² + x + 1 with ax² + bx + c,

a = 1,   b = 1,   c = 1

Step 1: Find α + β and αβ

α + β = −b/a = −1/1 = −1

αβ = c/a = 1/1 = 1

Step 2: Find 1/α + 1/β

1/α + 1/β = (α + β)/(αβ)

= (−1)/1

= −1

Final Answer

1/α + 1/β = −1

Conclusion

Hence, if α and β are the zeros of the polynomial f(x) = x² + x + 1, then the value of 1/α + 1/β is −1.