1.

Consider, f(x)=(x+2a)(x+a-4)(a in R), g(x)=k(x^(2)+x)+3k+x(k in R) and h(x)=(1-sin theta)x^(2)+2(1-sin theta)x-3 sin theta ( theta in R-(4n+1)(pi)/(2), n in I) If g(x) gt-3 for all real x, then the values of k are given by

Answer»

`-1 LT K lt 1/11`
`-1 lt k lt 0`
`0 lt k lt 1/22`
`k lt 1/11`

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