If alfa and bita are the zeroes of p(x)= X² -8x+ k and alfa SQ + bita SQ =40 then find the value of k.
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a=x
b=-8
c=k
Product of the zeroes=c/a
αβ=k (1)
Sum of the zeroes=-b/a
α+β=-(-8)/1
α+β=8
Squaring on both sides,
(α+β)²=(8)²
α²+β²+2αβ=64
40+2k=64 [Given that α² and β²=40 and from (1)]
2k=64-40
k=24/2
k=12
b=-8
c=k
Product of the zeroes=c/a
αβ=k (1)
Sum of the zeroes=-b/a
α+β=-(-8)/1
α+β=8
Squaring on both sides,
(α+β)²=(8)²
α²+β²+2αβ=64
40+2k=64 [Given that α² and β²=40 and from (1)]
2k=64-40
k=24/2
k=12
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