if α,β are the zeroes of a polynomial, such that α+β=10 and αβ=6, then write the polynomial.
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Answers
Answered by
6
α+β=-b/a
αβ=c/a
∴α+β=10 and αβ=6 (given)
so the polynomial will be a=1,b=-10,c=6
x²-10x+6=0 is the required polynomial..
αβ=c/a
∴α+β=10 and αβ=6 (given)
so the polynomial will be a=1,b=-10,c=6
x²-10x+6=0 is the required polynomial..
Janvichoudhari:
I was not able to find the answer the Answer thank you for your help
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Answered by
9
Hey !
α and β are the zeroes of a polynomial
given :-
sum of zeros = α + β=10
product of zeros = αβ = 6
We can form a polynomial , with the help of the given conditions ;-
k{ x² - (sum of zeros)x + (product of zeros)}
here , k is a constant , and can have any value like 1,2,3 .....
If k = 1 , and by substituting the rest of the values , we get the polynomial as:-
x² - 10x + 6 ----> required polynomial
α and β are the zeroes of a polynomial
given :-
sum of zeros = α + β=10
product of zeros = αβ = 6
We can form a polynomial , with the help of the given conditions ;-
k{ x² - (sum of zeros)x + (product of zeros)}
here , k is a constant , and can have any value like 1,2,3 .....
If k = 1 , and by substituting the rest of the values , we get the polynomial as:-
x² - 10x + 6 ----> required polynomial
k is a constant
ya I know that
if , there is a fraction in the sum of zeros , or product of zeros , we multiply the whole equation with tht constant
for example , we know tht sum of zeros of a polynomial is 1/4 and product of zeros is 6
the polynomial would be x2 - 1/4x + 6
OK sort of a different step than mine
to make this polynomial look simpler , we multiply the whole equation with a constant
ok thanks
k = 4 , then the equation becomes , 4x2 - x + 24
'-'
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