Question

the expression 2x^3+ax^2+bx-2 leaves remainder 7 and 0 when divided by 2x-3 and x+2 respectively calculate the value of a and b

Answer 1

When f(x) =2x-3=0,
x=3/2
f(3/2)=2*3/2*3/2*3/2+a*3/2*3/2+b*3/2-2=7
Or, 2*27/8+a*9/4+3b/2=9
Or,27/4+9a/4+3b/2=9
Or, 27+9a+6b/4=9
Or, 27+9a+6b=36
Or,9a+6b=9
Or,3(3a+2b)=9
Or,3a+2b=3....(i)


When f(x) =x+2=0
x=-2.
f(-2)=2*-2*-2*-2+a*-2*-2+b*-2 - 2=0
Or,-16+4a-2b=2
Or,4a-2b=18
Or,2(2a-b)=18
2a-b=9.....(ii)

Now, by evaluating simultaneously, I and II,
3a+2b=3}x1
2a-b=9}x2

3a+2b=3
4a-2b=18
-------------
=>7a=21
=>a=3
Substituting a in I,
3*3+2b=3
2b=3-9
2b=-6
b=-3


Therefore, a is 3 and b is - 3.

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Answer 2

Answer:

a=3 ,b=-3

Step-by-step explanation:

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