If x+1 is the factor of 2x3+ ax2+2bx +1 then find the value of a and b given that 2a-3b=4
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→ ans: a = 5 and b = 2
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p(x)=2x^3+ax^2+2bx+1
g(x)=x+1
By factor theorm,
x+1=0
x= -1
So, p(-1)=2*(-1)^3+a*(-1)^2+2*b*(-1)+1=0
2*(-1)+a-2b+1=0
-2+a-2b+1=0
a=1+2b---------(i)
given,
2a-3b=4
2*(1+2b)-3b=4 ( using (i) )
1+4b-3b=4
b=4-1=3
from (i),
a=2+2b
=2+2*3=2+6=8
So, a=8,b=3
g(x)=x+1
By factor theorm,
x+1=0
x= -1
So, p(-1)=2*(-1)^3+a*(-1)^2+2*b*(-1)+1=0
2*(-1)+a-2b+1=0
-2+a-2b+1=0
a=1+2b---------(i)
given,
2a-3b=4
2*(1+2b)-3b=4 ( using (i) )
1+4b-3b=4
b=4-1=3
from (i),
a=2+2b
=2+2*3=2+6=8
So, a=8,b=3
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