what is Lucas test, dont spam
Answers
Answer:
factorise completely the following polynomial 3x
3
+2x
2
−19x+6
Medium
Video Explanation
Solution To Question ID 578138
Answer
Let f(x)=3x
2
+2x
2
−19x+6
Using hit and trial method,
f(1)=3+2−19+6
=0
f(−1)=−3+2+19+6
=0
f(2)=24+8−38+6=0
∴(x−2) is a factor of f(x).
3x
2
+8x−3
Now, x−2
)3x
2
+2x
2
−19x+6
3x
2
−6x
----------------------------------
8x
2
−19x
8x
2
−16x
------------------------------------
−3x+6
−3x+6
-------------------------------------
x
--------------------------------------
To factorise 3x
2
+8x−3
=3x
2
+9x−x−3
=3x(x+3)−1(x+3)
=(3x−1)(x+3)
Hence 3x
3
+2x
3
−19x+6=(x−2)(3x−1)(x+3)
Answer verified by Toppr
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The Lucas test in alcohols is a test to differentiate between primary, secondary, and tertiary alcohols. It is based on the difference in reactivity of the three classes of alcohols with hydrogen halides via an SN1 reaction: ROH + HCl → RCl + H2O.An equimolar mixture of ZnCl2 and concentrated HCl is the reagent