If (2x + 1) is a factor of 6x + 5x + ax - 2, find the value of a.
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Given
f(x)=6x
3
+5x
2
+ax−2
Let us assume
2x+1=0⇒2x=−1⇒x=−
2
1
Since, (2x+1) is a factor of f(x) [Given]
∴ By factor theorem,
f(−
2
1
)=0
⇒6(−
2
1
)
3
+5(−
2
1
)
2
+a(−
2
1
)−2=0
⇒6(−
8
1
)+5(
4
1
)−(−
2
1
)−2=0
⇒−
4
3
+
4
5
−
2
a
−2=0
⇒−3+4−2a−8=0
⇒−6−2a=0
⇒2a=−6
⇒a=−3
Therefore, the value of a is –3.
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