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Q.
Find the least integral value of $k$ for which the quadratic trinomial $P(x)=(k-2) x^2+8 x+k+4$ is non-negative for all real values of $x$
Complex Numbers and Quadratic Equations
Solution:
$ k -2>0 \text { and } D \leq 0$
$k >2 $ ....(1) and
$64-4( k -2)( k +4) \leq 0 $
$16-\left( k ^2+2 k -8\right) \leq 0 $
$k ^2+2 k -24 \geq 0 $
$( k +6)( k -4) \geq 0 $ ....(2)
$\therefore(1) \cap(2) \Rightarrow k \geq 4$
