If α and β are the zeros of the quadratic polynomial f(x) = 6x² + x − 2, find the value of (α/β + β/α)

Video Explanation

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Solution

Given polynomial:

f(x) = 6x² + x − 2

Step 1: Find α + β and αβ

Comparing f(x) = 6x² + x − 2 with ax² + bx + c:

a = 6,   b = 1,   c = −2

α + β = −b/a = −1/6

αβ = c/a = −2/6 = −1/3

Step 2: Find the Required Value

α/β + β/α

= (α² + β²)/αβ

= {(α + β)² − 2αβ}/αβ

= {(−1/6)² − 2(−1/3)}/(−1/3)

= (1/36 + 2/3)/(−1/3)

= (25/36)/(−1/3)

= −25/12

Final Answer

The required value is −25/12.

Conclusion

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