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We have,
p(x) = x² − 6x + k ...........(1)
Since, α and β are the zeroes of the given polynomial.
So, α+β=6
αβ=k
Since,
a² + β² = 40
We know that,
(α+β)² = α² +β² +2αβ
6² - 40 + 2k
36 = 40 + 2k
−4 = 2k
k = −2
Hence, this is the answer.
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