Let (x−2) is a factor of the given expression.
x−2‌=0
x‌=2
Given: 2x3+ax2+bx−14=0
2(2)3+a(2)2+b(2)−14‌=0
16+4a+2b−14‌=0
4a+2b+2‌=0
4a+2b‌=−2
2a+b‌=−1‌‌...‌ (i) ‌
and when given expression is divided by (x−3) .
x−3‌=0
x‌‌=3
∴‌‌2x3+ax2+bx−14‌=52
2(3)3+a(3)2+b(3)−66‌=0
54+9a+3b−66‌=0
9a+3b‌=12
3a+b=4 ............(ii)
Solving equation (i) and (ii),
‌2a+b=−1
‌3a+b=4
(−)(−)‌‌(−)
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−a=−5‌‌⇒a=5
from (ii),
3×5+b‌=4
b‌=4−15=−11
∴‌‌a=5‌ and ‌b=−11