JEE Mains · Maths · STD 12 - 13. probability
The coefficients \(a, b\) and \(c\) of the quadratic equation, \(ax ^{2}+ bx + c =0\) are obtained by throwing a dice three times. The probability that this equation has equal roots is
- A \(\frac{1}{72}\)
- B \(\frac{5}{216}\)
- C \(\frac{1}{36}\)
- D \(\frac{1}{54}\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{216}\)
Step-by-step Solution
Detailed explanation
\(a x^{2}+b x+c=0\) For equal roots \(D=0\) \(\Rightarrow b ^{2}=4 ac\) Case \(I : ac =1\) \(( a , b , c )=(1,2,1)\) Case \(II : ac = 4 ( a , b , c )=(1,4,4)\) or \((4,4,1)\) or \((2,4,2)\) Case \(III : ac = 9\) \(( a , b , c )=(3,6,3)\) Required probability \(=\frac{5}{216}\)
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