Zadanie 2
Solve 2 ⋅ 16x + 7 ⋅ 4x − 4 = 0 over the reals.
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Solve 2 ⋅ 16x + 7 ⋅ 4x − 4 = 0 over the reals.
Verify that the mean y is 14.
Find p and q.
Explain why the generator has 128 possible quadratics.
Verify that the allowed choice a=4,b=8,c=4 gives a graph with exactly one x-intercept.
Show that the probability of exactly one x-intercept is 3/64.
For generated quadratics with two distinct x-intercepts, determine the possible values of ac.
For quadratics with two distinct x-intercepts: (i) show that ac=1 gives six possible quadratics; (ii) show that ac=2 gives twelve.
Find the probability p that a generated quadratic has two distinct x-intercepts. Show how you count the possibilities.
Now use the continuous model q(x) = x2 + 2Zx + 4, where Z is normal with mean 0.5 and standard deviation 1.5. Find the probability of two distinct x-intercepts.