find quadratic polynomial 1/3,-1 as the sum and product oF it's zero resp.
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find quadratic polynomial 1/3,-1 as the sum and product oF it's zero resp.
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Answer:
k( 3x²-1x-3 )
Explanation:
We have,
Sum of the Zeros = 1/3
Product of the zeros = -1
So the quadratic equation is
= k( x² - (sum of zeros)x + product of zeros)
= k( x² - 1/3x -1)
= k( 3x²-1x-3)
where k is a constant.
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Given:-
To find:-
Solution:-
we know,
Skeletal quadratic polynomial:-
[tex] {x}^{2} - (sum \: of \: zereos)x + product \: of \: zeroes)[/tex]
Now,
By putting the given value,we get
[tex] {x }^{2} - \frac{1}{3} x + ( - 1)[/tex]
[tex] = {x}^{2} - \frac{1}{3} x - 1[/tex]
[tex] = 3 {x}^{2} - x - 3[/tex]
Hence,the required polynomial is
[tex]3 {x}^{2} - x - 3[/tex]
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