If x3 + px2 + qx + 5 has (x – 1) as a factor an leaves a remainder 3 when divided by (x -2), find the values of p and q.
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Answer:
p=1 q=-7
Step-by-step explanation:
f(x)=x³+px²+qx+5
f(1)=1³+p(1²)+q(1)+5
=1+p+q+5
=p+q+6
As x-1 is a factor so
f(1)=0
p+q+6=0. eq(1)
now
f(2)=2³+(2)²p+(2)q+5
=8+4p+2q+5
=4p+2q+13
as f(2)=3
so.
4p+2q+13=3
4p+2q+13-3=0
4p+2q+10=0. eq(2)
from eq1 let
p=-q-6. eq(3)
put in eq2
4(-q-6)+2q+10=0
-4q-24+2q+10=0
-2q-14=0
-2q=14
q=14/-2
q=-7
put in eq3.
p=-(-7)-6
p=+7-6
p=1
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