If α and β are the zeros of f(x) = x² − 5x + 4, find the value of (1/α + 1/β − 2αβ)

Video Explanation

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Solution

Given polynomial:

f(x) = x² − 5x + 4

Step 1: Find α + β and αβ

Comparing f(x) = x² − 5x + 4 with ax² + bx + c:

a = 1,   b = −5,   c = 4

α + β = −b/a = 5

αβ = c/a = 4

Step 2: Find (1/α + 1/β)

1/α + 1/β = (α + β)/αβ

= 5/4

Step 3: Find the Required Value

1/α + 1/β − 2αβ

= 5/4 − 2 × 4

= 5/4 − 8

= (5 − 32)/4

= −27/4

Final Answer

The required value is −27/4.

Conclusion

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