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[SOLVED] IB23. A family of functions is given by...calculate the probability


Well-known member
Jan 31, 2012
View attachment 1183

well by completing the square from $x^2+3x$ we get $\pmatrix {x+\frac{3}{2}}^2 -\frac{9}{4}$
which means the vertex is more than $2$ below the x-axis but above at $3$

so from the set k only at $k=1$ and $k=2$ will it cross the x-axis so $\frac{2}{7}$ is the probability that the function will cross the x-axis.

one way i guess


Active member
Feb 9, 2012
You could also use the discriminant of f(x).

$3^2 - 4k > 0$

Works only for k = 1 . k = 2



Staff member
Feb 24, 2012
While completing the square certainly works, I agree with agentmulder's suggestion of using the discriminant as a means to determine when there will be two distinct real roots. It seems more straightforward to me.