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Sia ? 6 years ago
Since, α and β are the zeroes of the quadratic polynomial
f(x) = x2 - p (x+1) - c=x2-px-(p+c)
So A=1 B=-p,C=-(p+c)
Sum of the zeroes α + β = −BA=P
Product of the zeroes αβ =CA=- (p + c)
(α + 1)(β + 1)
= αβ + α + β + 1
= αβ + (α + β) + 1
=-(p+c)+p+1
=-p-c-p+1
=1-c
Hence proved
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Sia ? 6 years ago
Let PM be the light house of height 200 m and let A and B be two ships on the either sides of lighthouse such that the angles of depression of A and B are 60o and 45o respectively.
Let, AM = x m and BM=y m
Then, ∠XPB=∠MBP=45o [alternate angle]
and ∠YPA=∠MAP=60o [alternate angles]
In right-angled △AMP, tan60o=PB=PMAM
⇒√3=200x
⇒x=200√3m
In right-angled △BMP, tan45o=PMBM
⇒1=200y
⇒y=200m
Now, distance between the two ships = AB = x+y=200+200√3=315.48m
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