Question

If 2x^3+ax^2+bx-2 leaves remainder 7 and 0 when divided by 2x-3 and x+2 respectively. Calculate the values of a and b.

Answer 1

HEY MATE...

HERE IS YOUR ANSWER...

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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