Polynomials and Probability

Orgasmic Troll · 2003-09-09, 16:00

CAUTION: This is more fun (?) math problem than puzzle

given P(x) = ax^2 + bx + c where a,b,c are random (uniformly distributed over the interval [-n,n]) what is the probability that P(x) has real roots?

eepiccolo · 2003-09-09, 16:45

Are a, b, and c independant?

Orgasmic Troll · 2003-09-09, 16:54

yes

Orgasmic Troll · 2003-09-16, 15:59

<bump>

xilman · 2003-09-16, 16:23

A quadratic polynomial has real roots if its discriminant is non-negative.

Thus the question boils down to: what is the probability that b² >= 4ac ?

I don't think I can go much further without giving too much away.

Paul

2003-09-09, 16:00	#1
Orgasmic Troll Cranksta Rap Ayatollah Jul 2003 641 Posts	Polynomials and Probability CAUTION: This is more fun (?) math problem than puzzle given P(x) = ax^2 + bx + c where a,b,c are random (uniformly distributed over the interval [-n,n]) what is the probability that P(x) has real roots?

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2003-09-09, 16:45	#2
eepiccolo Dec 2002 Frederick County, MD 562₈ Posts	Are a, b, and c independant?

2003-09-09, 16:54	#3
Orgasmic Troll Cranksta Rap Ayatollah Jul 2003 641 Posts	yes

2003-09-16, 15:59	#4
Orgasmic Troll Cranksta Rap Ayatollah Jul 2003 641 Posts	<bump>

2003-09-16, 16:23	#5
xilman Bamboozled! "𒉺𒌌𒇷𒆷𒀭" May 2003 Down not across 2×5×1,187 Posts	A quadratic polynomial has real roots if its discriminant is non-negative. Thus the question boils down to: what is the probability that b² >= 4ac ? I don't think I can go much further without giving too much away. Paul