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Find the Values of Constants a and B When X – 2 and X + 3 Both Are the Factors of Expression X3 + Ax2 + Bx – 12. - ICSE Class 10 - Mathematics

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Question

Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression x3 + ax2 + bx – 12.

Solution

Let `f(x)=x^3+ax^2+bx-12` 

`x-2=0`⇒x=2 

`x-2  " is  a factor of   f(x). so, remainder "=0` 

∴ `(2)^3+a(2^2)+b(2)-12=0` 

`8+4a+2b-12=0` 

⇒`4a+2b-4=0` 

⇒`2a+b-2=0`  .......... (1) 

x+3 = 0  ⇒ x = -3     

x+3 is a factor  of f(x). so, remainder =0 

∴ `(-3)^3+a(-3)^2+b(-3)-12=0` 

⇒`-27+9a-3b-12=0` 

⇒`9a-3b-39=0` 

⇒`3a-b-13=0`           .......................(2)

Adding (1) and (2), we get, 

`5a-15=0` 

⇒a=3 

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

 6+b-2=0 

⇒b=-4

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Solution Find the Values of Constants a and B When X – 2 and X + 3 Both Are the Factors of Expression X3 + Ax2 + Bx – 12. Concept: Factor Theorem.
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