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ICSE Class 10 Answered

Solve the equation x(x-1)(x-2)(x-3)+8=0
Asked by lovemaan5500 | 18 Feb, 2018, 09:21: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight x left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis left parenthesis straight x minus 3 right parenthesis plus 8 equals 0 Simplifying space it space you space get straight f left parenthesis straight x right parenthesis equals straight x to the power of 4 minus 2 straight x cubed minus 5 straight x squared plus 6 straight x plus 8 equals 0 Put space straight x equals 2 rightwards double arrow straight f left parenthesis straight x right parenthesis equals 0 Hence comma space left parenthesis straight x minus 2 right parenthesis space is space straight a space factor space of space the space given space polynomial. After space dividing space straight f left parenthesis straight x right parenthesis space by space straight x minus 2 comma straight f left parenthesis straight x right parenthesis equals left parenthesis straight x minus 2 right parenthesis left parenthesis straight x cubed minus 5 straight x minus 4 right parenthesis Let space straight h left parenthesis straight x right parenthesis equals straight x cubed minus 5 straight x minus 4 Put space straight x equals negative 1 rightwards double arrow straight h left parenthesis straight x right parenthesis equals 0 Hence comma space straight x plus 1 space is space straight a space factor space of space straight h left parenthesis straight x right parenthesis After space dividing space straight h left parenthesis straight x right parenthesis space by space straight x plus 1 space you space get straight h left parenthesis straight x right parenthesis equals left parenthesis straight x plus 1 right parenthesis left parenthesis straight x squared minus straight x minus 4 right parenthesis straight f left parenthesis straight x right parenthesis equals left parenthesis straight x minus 2 right parenthesis left parenthesis straight x plus 1 right parenthesis left parenthesis straight x squared minus straight x minus 4 right parenthesis equals 0 straight x equals 2 space or space straight x equals negative 1 space or space straight x squared minus straight x minus 4 equals 0 Find space straight x space using space quadratic space equation space formula. straight x equals fraction numerator 1 plus-or-minus square root of 17 over denominator 2 end fraction end style
Answered by Sneha shidid | 19 Feb, 2018, 09:12: AM

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