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| 1. |
if one zero of the polynomial p (×)=×2-6×2+11×-6is3,find other two zero |
| Answer» The given polynomial f(x)={tex}\\text{x}^3-\\text{6x}^2+\\text{11x-6}{/tex}Since 3 is a zero of p(x), so (x - 3) is a factor of f(x).On dividing f(x) by (x - 3), we get{tex}\\therefore{/tex}\xa0f(x) = (x2\xa0- 3x + 2)(x - 3)= ( x2\xa0- 2x - x + 2)( x - 3)= [x(x - 2) -1(x - 2)](x - 3)= (x - 1)(x - 2)(x - 3)Now f(x)=0 if x - 1 = 0 or x - 2 = 0 or x - 3 = 0{tex}\\Rightarrow{/tex}\xa0x = 1 or x = 2 or x = 3{tex}\\mathrm{Hence}\\;\\mathrm{the}\\;\\mathrm{remainig}\\;\\mathrm{roots}\\;\\;\\mathrm{of}\\;\\mathrm f(\\mathrm x)\\;\\mathrm{are}\\;1\\;\\mathrm{and}\\;2\\;{/tex} | |