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The Expression 2x3 + Ax2 + Bx – 2 Leaves Remainder 7 and 0 When Divided by 2x – 3 and X + 2 Respectively. Calculate the Values of a and B - CBSE Class 9 - Mathematics

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Question

The expression 2x3 + ax2 + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b

Solution

Left f(x)=`2x^3+ax^2+bx-2` 

`2x-3=0`   ⇒ `x=3/2` 

on dividing f(x) by 2x-3, it leaves a remainder 7 

∴ `2(3/2)^3 ++a(3/2)^2+b(3/2)-2=7`  

`27/4+(9a)/4+(3b)/2=9`  

`(27+9a+6b)/4=9` 

`27+9a+6b=36`  

`9a+6b-9=0` 

`3a+2b-3=0`          ................(1)

x+2=0  ⇒   x=-21

On dividing f(x) by  x+2, it leavves a remainder 0. 

∴`2(-2)^3+a(-2)^2+b(-2)-2=0` 

`-16+4a-2b-2=0` 

`4a-2b-18=0`         ...............(2)

Adding (1)and (2), we get,   

7a-21=0 

a=3 

Subsituting the value of a in (1), we get, 

3(3)+2b-3 =0 

9+2b-3=0 

2b=-6 

b=-3 

  Is there an error in this question or solution?
Solution The Expression 2x3 + Ax2 + Bx – 2 Leaves Remainder 7 and 0 When Divided by 2x – 3 and X + 2 Respectively. Calculate the Values of a and B Concept: Remainder Theorem.
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