If α and β are the zeroes of the quadratic polynomial f(x) = x² + x − 2, find the value of (1/α − 1/β)

Video Explanation

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Solution

Given polynomial:

f(x) = x² + x − 2

Step 1: Find α + β and αβ

Comparing f(x) = x² + x − 2 with ax² + bx + c:

a = 1,   b = 1,   c = −2

α + β = −b/a = −1

αβ = c/a = −2

Step 2: Find the Required Value

1/α − 1/β

= (β − α)/αβ

= (−2 − 1)/(−2)

= −3/(−2)

= 3/2

Final Answer

The required value is 3/2.

Conclusion

Thus, using the relationship between zeros and coefficients of the quadratic polynomial, the value of the given expression is correctly obtained.