if a beta are the two zeros of the polynomial f y is equal y square-8y+a and a square+beta squar is equal to 40 find the value of a
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Given :-
α and β are zeroes of f(y) = y² - 8y + a
To Find :-
Value of a
Solution :-
We know that
Sum of zeroes = -b/a
By putting value
α + β = -(-8)/1
α + β = 8/1
α + β = 8
Now
αβ = c/a
αβ = a/1
αβ = a
Now
(α + β) = 40
α² + β² + 2αβ = 40
Taking 2 as common
(α + β)² + 2αβ = 40
(8)² + 2(a) = 40
(64) + 2a = 40
2a = 64 - 40
2a = 24
a = 24/2
a = 12
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