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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

ConceptRemainder Theorem

#### 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)

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

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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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