3. If 2x3 + ax2 + bx - 6 has a factor (2x + 1) and
+,
leaves the remainder 12 when divided by (x + 2).
Calculate the values of a and b, hence factorise the
expression completely.
Answers
Answered by
6
Answer:
a=57/5
b=29/5
Step-by-step explanation:
Let p(x) = 2x³+ ax²+ bx - 6 has a factor (2x + 1)
taking 2x+1=0
x=-1/2
Then p(-1/2)=0
2*(1/2)³+a(1/2)²+b*1/2-6=0
2/8 + a/4 +b/2-6=0
2+2a+4b-48=0
2a+4b=46........................(1)
Now p(x) leaves the remainder 12 when divided by (x + 2).
so x+2=0,x=-2
Thus from remainder theorem
p(-2)=12
or 2*(-2)³+a*(-2)²+b(-2)-6=12
-16+4a-2b-6=12
4a-2b=34
Or 2a-b=17............................(2)
Subtracting (2) from(1)
4b+b=46-17=29
b=29/5
From(2)
2a-29/5=17
10a-29=85
10a=114
a=114/10=57/5
Answered by
2
Answer:
a = 57/5
b = 29/5
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