goooood

suppose f(x)=x³+ax²+bx+c a,b,c are chosen respectively by throwing die three times.Find probability that f(x) is inc. function

ans=5/12

1 Answers

f(x)=x3+ax2+bx+c

f'(x)=3x²+2ax+b
for increasing, this is >=0 for all x

so this has to have no real roots!

so (2a)²<4.3.b

a²<3b

if b=1, a=1
b=2, a=1,2
b=3, a=1,2
b=4, a=1,2,3
b=5, a=1,2,3
b=6, a=1,2,3,4

favorable cases=15

total cases =36

Note (we din have to worry about c!!)

hence P=15/36

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