find the polynomial whose zeros are 3 and -4
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find the polynomial whose zeros are 3 and -4
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Answer :-
The polynomial whose zeroes are 3 and - 4 is x² + x - 12.
Solution :-
Given
Zeroes of a polynomial are 3 and - 4
So
• α = 3
• β = - 4
Now, find the sum of zeroes and product of zeroes
Sum of zeroes = α + β
= 3 + (-4)
= 3 - 4
= - 1
Product of zeroes = αβ
= 3(-4)
= - 12
Quadratic polynomial ax² + bx + c = k[x² - x(α + β) + αβ]
(Where k ≠ 0)
Here
• α + β = - 1
• αβ = - 12
By substituting the values
= k[x² - x(-1) + (-12)]
= k(x² + x - 12)
When k = 1
= 1(x² + x - 12)
= x² + x - 12
Therefore the polynomial whose zeroes are 3 and - 4 is x² + x - 12.