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Q.The number of points(b,c)lying on the circle x^2+(y-3)^2=8 such that the quadratic equation t^2+by+c=0 has real roots is 
Asked by Vidushi412 | 13 Mar, 2019, 11:36: AM
answered-by-expert Expert Answer
Quadratic equation y2 +by+c =0 has real roots if b2 = 4c   ...........(1)
 
if (b.c ) is on circle x2 +(y-3)2 = 8  ,  then we have,  b2 +(c-3)2 = 8  ..............(2)
 
let us use eqn.(1) in eqn.(2) and rewrite as :  4c +(c-3)2 = 8   or  c2 -2c +1 = 0   or  (c-1)2 = 0  or  c = 1
 
if we use the value of c in eqn.(1), we get b = +2 or -2
 
hence we have 2 points (2, 1)   and (-2, 1) on the circle satisfying the required condition
Answered by Thiyagarajan K | 13 Mar, 2019, 18:10: PM

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