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If both x + 1 and x - 1 are factors of ax3 + x2 - 2x + b, find the value of a and b. |
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Answer» Let, f (X) = ax3 + x2 - 2x + b be the given polynomial. Given (x + 1) and (x – 1) are factors of f (x). From factor theorem, If (x + 1) and (x – 1) are factors of f (x) then f (-1) = 0 and f (1) = 0 respectively. f (-1) = 0 a (-1)3 + (-1)2 – 2 (-1) + b = 0 - a + 1 + 2 + b = 0 - a + 3 + b = 0 b – a + 3 = 0 (i) f (1) = 0 a (1)3 + (1)2 – 2 (1) + b = 0 a + 1 – 2 + b = 0 a + b – 1 = 0 b + a – 1 = 0 (ii) Adding (i) and (ii), we get b – a + 3 + b + a – 1 = 0 2b + 2 = 0 2b = - 2 b = - 1 Putting value of b in (i), we get - 1 - a + 3 = 0 - a + 2 = 0 a = 2 Hence, the value of a = 2 and b = - 1. |
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