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CBSE Class 12-science Answered

Consider the two equations x2 + Px + 2 = 0 and x2 + 2x + P = 0. Find the sum of the all possible values of P for which the equations have atleast one common real root.
Asked by pooja1994surya | 09 Sep, 2020, 02:26: PM
answered-by-expert Expert Answer
Conditions for the roots to be common is
open vertical bar table row cell straight a subscript 1 end cell cell straight c subscript 1 end cell row cell straight a subscript 2 end cell cell straight c subscript 2 end cell end table close vertical bar squared equals open vertical bar table row cell straight a subscript 1 end cell cell straight b subscript 1 end cell row cell straight a subscript 2 end cell cell straight b subscript 2 end cell end table close vertical bar open vertical bar table row cell straight b subscript 1 end cell cell straight c subscript 1 end cell row cell straight b subscript 2 end cell cell straight c subscript 2 end cell end table close vertical bar open vertical bar table row 1 2 row 1 straight P end table close vertical bar squared equals open vertical bar table row 1 straight P row 1 2 end table close vertical bar open vertical bar table row straight P 2 row 2 straight P end table close vertical bar open parentheses straight P minus 2 close parentheses squared equals open parentheses 2 minus straight P close parentheses open parentheses straight P squared minus 4 close parentheses open parentheses straight P minus 2 close parentheses squared equals negative open parentheses straight P minus 2 close parentheses open parentheses straight P minus 2 close parentheses open parentheses straight P plus 2 close parentheses open parentheses straight P minus 2 close parentheses squared equals negative open parentheses straight P minus 2 close parentheses squared open parentheses straight P plus 2 close parentheses open parentheses straight P minus 2 close parentheses squared open square brackets 1 plus straight P plus 2 close square brackets equals 0 rightwards double arrow straight P equals 2 space or space 1 plus straight P plus 2 equals 0 rightwards double arrow straight P equals 2 space or space straight P equals negative 3 Sum space of space values space of space straight P space equals space 2 minus 3 equals negative 1
Answered by Renu Varma | 10 Sep, 2020, 11:02: AM

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