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If Both X + 1 and X − 1 Are Factors of Ax3 + X2 − 2x + B, Find the Values of a and B. - Mathematics

Answer in Brief

If both x + 1 and x − 1 are factors of ax3 + x2 − 2x + b, find the values of a and b.

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Solution

Let  f(x) = ax3 + x2 − 2x + b be the given polynomial.

By factor theorem, if (x+1) and  (x-1)both are factors of the polynomial f (x). if f(−1) and f(1) both are equal to zero.

Therefore,

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

                                        ` -a + 1+ 2+b =0`

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

And

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

`a+1 -2 + b = 0`

               `a+b = 1     ......... (2)`

Adding (i) and (ii), we get

 2b =-2

b =-1

And putting this value in equation (ii), we get,

a = 2

Hence, the value of a and b are 2 and −1 respectively.

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 6 Factorisation of Polynomials
Exercise 6.4 | Q 22 | Page 25
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