Saved Bookmarks
| 1. |
If both (x+1) and (x-1) are factors of ax3 +x2 -2x +b, find ‘a’ and ‘b’ |
|
Answer» f(x) =ax^3 + x^2 -2x + b x+1 is a factor Applying factor theorem, x + 1 = 0 x = -1 f(-1) = 0 a(-1)^3 +(-1)^2 -2(-1) + b = 0 -a + 1 + 2 + b = 0 b - a + 3 = 0 b = a - 3 (equation 1) x - 1 is a factor Applying factor theorem x - 1 = 0 x = 1 f(1) = 0 a(1)^3 + (1)^2 - 2(1) + b = 0 a + 1 - 2 + b = 0 a + b - 1 = 0 a + b = 1 (equation 2) substitute equation 1 into equation 2 a + a - 3 = 1 2a = 1 + 3 2a = 4 a = 4/2 a = 2 b = a - 3 b = 2 - 3 b = -1 |
|