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

Video Explanation

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Solution

Given polynomial:

f(x) = x² − x − 4

Step 1: Find α + β and αβ

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

a = 1,   b = −1,   c = −4

α + β = −b/a = 1

αβ = c/a = −4

Step 2: Find the Required Value

1/α + 1/β − αβ

= (α + β)/αβ − αβ

= 1/(−4) − (−4)

= −1/4 + 4

= (−1 + 16)/4

= 15/4

Final Answer

The required value is 15/4.

Conclusion

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