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CBSE Class 10 Answered

If the zeroes of polynomial  x^4-6x^3-26x^2+138x-35 are 2+root3 and 2-root3, find other zeroes.
Asked by arindeep.singh | 26 Jun, 2020, 03:38: PM
answered-by-expert Expert Answer
4.
Given polynomial is p(x) = x4 - 6x3 - 26x2 + 138x - 35
The two zeroes are already given, let the other two zeroes be a and b
Using the relation between zeroes and the coefficients, we have
ab open parentheses 2 plus square root of 3 close parentheses open parentheses 2 minus square root of 3 close parentheses equals negative 35 ab open parentheses 4 minus 3 close parentheses equals negative 35 ab equals negative 35 space... space left parenthesis straight i right parenthesis Also comma straight a plus straight b plus 2 plus square root of 3 plus 2 minus square root of 3 equals negative open parentheses negative 6 close parentheses equals 6 straight a plus straight b plus 4 equals 6 straight a plus straight b equals 2 rightwards double arrow straight a equals 2 minus straight b From space left parenthesis straight i right parenthesis open parentheses 2 minus straight b close parentheses straight b equals negative 35 rightwards double arrow straight b squared minus 2 straight b minus 35 equals 0 rightwards double arrow straight b squared minus 7 straight b plus 5 straight b minus 35 equals 0 rightwards double arrow straight b left parenthesis straight b minus 7 right parenthesis plus 5 left parenthesis straight b minus 7 right parenthesis equals 0 rightwards double arrow left parenthesis straight b minus 7 right parenthesis left parenthesis straight b plus 5 right parenthesis equals 0 rightwards double arrow straight b equals 7 space space or space space straight b equals negative 5 When space straight b equals 7 rightwards double arrow straight a equals negative 5 When space straight b equals negative 5 space rightwards double arrow space straight a equals 7 Hence comma space the space two space roots space are space minus 5 space and space 7.
Answered by Renu Varma | 28 Jun, 2020, 04:47: PM

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