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please explain question 4 and 5 both

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Asked by arindeep.singh | 24 Jun, 2020, 10:21: PM

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 | 26 Jun, 2020, 05:05: PM

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