If α and β are the zeros of the quadratic polynomial p(y) = 5y² − 7y + 1, find the value of (1/α + 1/β)

Video Explanation

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Solution

Given polynomial:

p(y) = 5y² − 7y + 1

Step 1: Find α + β and αβ

Comparing p(y) = 5y² − 7y + 1 with ay² + by + c:

a = 5,   b = −7,   c = 1

α + β = −b/a = 7/5

αβ = c/a = 1/5

Step 2: Find the Required Value

1/α + 1/β = (α + β)/αβ

= (7/5) ÷ (1/5)

= 7

Final Answer

The required value is 7.

Conclusion

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