# Let `f(x) = x^2+2x+9; x in RR` Determine the set of values of a real constant `lambda` for which the equation `f(x)=lambda` ; that f(x) has no real solution for x.

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Expert Answers

jeew-m | Certified Educator

`f(x) = x^2+2x+9`

`x^2+2x+9 = lambda`

`x^2+2x+9-lambda = 0`

If the above quadratic function does not have real roots then the discriminant(Delta) should be less than 0.

`Delta = 4-4xx1xx(9-lambda)<0`

`4<4(9-lambda)`

`lambda<8`

** So for `f(x) = lambda` where there is no solutions **`lambda<8`

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