If a, b,y are the zeroes of the cubic polynomial 2x3 - 3x2 + 6x + 1 then find the value of
40² + 4B² + 4y²
Answers
Answered by
0
Answer:
If α is the root of 2x
3
−3x
2
+6x+6=0 find [α].
∵2x
3
−3x
2
+6x+6=0
f
′
(x) =
dx
d
(2x
3
−3x
2
+6x+6)
=x
2
−x+6
=6(x
2
+x−1)
∵ Discriminent of f
′
(x)<0
Hence f
′
(x) is always greater than 0.
Hence f(x) is an increasing function, which means that it has only one root.
Let x=−1
f(−1)=2(−1)
3
−3(−1)
2
+6(−1)+6
=−2−3−6+6
=−5
Let x=0
f(−1)=2(0)
3
−3(0)
2
+6(0)+6
=6
Hence f(−1)f(0)<0
Which means that α should be in between −1 & 0.
Hence [α]=−1
Similar questions