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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

#### 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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