Find the polynomial whose sum of zeros and product
of zeros are 7/3 and 5/3 respectively.
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Answer :-
The polynomial is 3x² - 7x + 5.
Solution :-
Given
Sum of zeroes = α + β = 7/3
Product of zeroes = αβ = 5/3
We know that
Quadratic polynominal ax² + bx + c = k[x² - x(α + β) + αβ]
(Where k ≠ 0)
By substituting the given values
= k[x² - x(7/3) + 5/3]
= k[x² - 7x/3 + 5/3]
Taking LCM
= k[(3x² - 7x + 5)/3]
When k = 3
= 3[(3x² - 7x + 5)/3]
= 3x² - 7x + 5
Therefore the polynomial is 3x² - 7x + 5.
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