If α and β are the zeros of the polynomial p(x) = 4x² + 3x + 7, find the value of 1/α + 1/β
Video Explanation
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Given
p(x) = 4x² + 3x + 7
α and β are the zeros of the polynomial.
To Find
The value of 1/α + 1/β.
Solution
For a quadratic polynomial ax² + bx + c:
Sum of zeros, α + β = −b/a
Product of zeros, αβ = c/a
Comparing p(x) = 4x² + 3x + 7 with ax² + bx + c,
a = 4, b = 3, c = 7
Step 1: Find α + β and αβ
α + β = −b/a = −3/4
αβ = c/a = 7/4
Step 2: Find 1/α + 1/β
1/α + 1/β = (α + β)/(αβ)
= (−3/4)/(7/4)
= −3/7
Final Answer
1/α + 1/β = −3/7
Conclusion
Hence, if α and β are the zeros of the polynomial p(x) = 4x² + 3x + 7, then the value of 1/α + 1/β is −3/7.