If α and β are the zeroes of the quadratic polynomial f(x) = ax² + bx + c, find the value of (1/α + 1/β − 2αβ)

Video Explanation

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Solution

Given polynomial:

f(x) = ax² + bx + c

Let α and β be the zeroes of the given quadratic polynomial.

Step 1: Write the Known Relations

For a quadratic polynomial ax² + bx + c:

α + β = −b/a

αβ = c/a

Step 2: Evaluate Each Term

1/α + 1/β = (α + β)/αβ

= (−b/a) ÷ (c/a)

= −b/c

2αβ = 2(c/a)

Step 3: Find the Required Value

1/α + 1/β − 2αβ

= −b/c − 2c/a

Final Answer

The required value is −b/c − 2c/a.

Conclusion

Thus, using the relationship between zeroes and coefficients of the quadratic polynomial, the value of (1/α + 1/β − 2αβ) is −b/c − 2c/a.