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CBSE Class 10 Answered

If a and 1/a are the zeros of the polynomial 4 x squared minus 2 x plus left parenthesis k minus 4 right parenthesis ,find the value of "k".
Asked by Vinaymehra.mehra | 27 Jan, 2019, 06:00: PM
answered-by-expert Expert Answer
f(x) = 4x2 -2x+(k-4) = 0
 
f(a) = 4a2 -2a +(k-4) = 0  ...............(1)
 
f(1/a) = ( 4/a2) - (2/a) + (k-4) = 0 ...............(2)
 
By equating (1) and (2), 4a2 -2a = ( 4/a2) - (2/a)   or  4a2 -2a -( 4/a2) + (2/a) = 0  or 2a4 -a3 +a2 -2 = 0 ..............(3)
 
eqn.(3) has solution a =1. If we substitute a=1 in eqn.(1), we get k =2
Answered by Thiyagarajan K | 27 Jan, 2019, 08:02: PM
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