Let `f(x) = x^2+2x+9; x inRR` Find the value of a real constant k for which the equation f(x)=k has exactly one real roots for x.

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If any quadratic polynomial has real one single root the the discriminant of the quadratic equation is 0.

`f(x) = k`

`x^2+2x+9 = k`

`x^2+2x+(9-k) = 0`

Discriminant `(Delta) = 4-4xx1xx(9-k) = 0`

`4-4xx1xx(9-k) = 0`

`k-9 = -1`

`k = 8`

So for exactly one real root the value of k should be 8.

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