if alpha , beta are the two zeroes of the quadratic polynomial x^2 - 8x + k and (alpha)^2 + (beta)^2 = 40 find the value of k.
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∵ α & β are zeroes
∴ α + β = -b/a
α.β=c/a
in p(x)= x² - 8x + k
a=1; b=-8; c=k
∴ α + β = -(-8)/1 = 8 ................................... (i)
α.β= k/1 = k .................................................(ii)
Squaring eq. (i)
(α + β)² = 8²
α² + β² + 2αβ = 64
40 + 2αβ = 64 .......................................................(∵ Given α²+β²=40)
2αβ = 24
αβ = 12
From eq(ii)
k = 12
HOPE IT HELPS.......................... :)
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Hope it is correct.......
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satkr99:
actually a^2+b^2 =(a+b)^2 -2ab
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