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

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: Use the Identity for (α − β)²

(α − β)² = (α + β)² − 4αβ

= (−b/a)² − 4(c/a)

= b²/a² − 4c/a

= (b² − 4ac)/a²

Step 3: Find the Value of α − β

Taking square root on both sides:

α − β = √(b² − 4ac)/a

Final Answer

The value of α − β = √(b² − 4ac) / a.

Conclusion

Thus, the difference of the zeroes of the quadratic polynomial ax² + bx + c is √(b² − 4ac) / a.