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CBSE Class 10 Answered

The equations x square - 4x + k= 0 and x square + kx - 4 =0, where k is a real number, have exactly one common root. What is the value of k?
Asked by vikasg13.hardware | 13 Jun, 2018, 11:41: AM
answered-by-expert Expert Answer
begin mathsize 16px style straight x squared minus 4 straight x plus straight k equals 0............ left parenthesis straight i right parenthesis
straight x squared plus kx minus 4 equals 0............ left parenthesis ii right parenthesis
Both space the space equations space have space one space common space root.
Let space straight b space is space the space common space root space of space the space equation space of space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
straight b squared space minus 4 straight b plus straight k equals 0............ left parenthesis iii right parenthesis
straight b squared plus kb minus 4 equals 0............. left parenthesis iv right parenthesis
Subtracting space left parenthesis iv right parenthesis space from space left parenthesis iii right parenthesis
straight b squared space minus 4 straight b plus straight k space minus open parentheses straight b squared plus kb minus 4 space close parentheses equals 0
minus 4 straight b plus straight k minus kb plus 4 equals 0
minus straight b left parenthesis straight k plus 4 right parenthesis plus left parenthesis straight k plus 4 right parenthesis equals 0
left parenthesis straight k plus 4 right parenthesis left parenthesis 1 minus straight b right parenthesis equals 0
rightwards double arrow straight b equals 1
Put space straight b equals 1 space in space left parenthesis iii right parenthesis
1 squared space minus 4 cross times 1 plus straight k equals 0
1 minus 4 plus straight k equals 0
minus 3 plus straight k equals 0
straight k equals 3

end style
Answered by Sneha shidid | 13 Jun, 2018, 03:57: PM
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