JEE Mains · Maths · STD 12 - 13. probability
The coefficients \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) in the quadratic equation \(a x^2+b x+c=0\) are chosen from the set \(\{1,2,3,4,5,6,7,8\}\). The probability of this equation having repeated roots is :
- A \(\frac{3}{256}\)
- B \(\frac{1}{128}\)
- C \(\frac{1}{64}\)
- D \(\frac{3}{128}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{64}\)
Step-by-step Solution
Detailed explanation
\( a x^2+b x+c=0 \) \( a, b, c \in\{1,2,3,4,5,6,7,8\} \) Repeated roots \( D=0 \) \( \Rightarrow b^2-4 a c=0 \Rightarrow b^2=4 a c \) Prob \(=\frac{8}{8 \times 8 \times 8}=\frac{1}{64} \) \( \Rightarrow(a, b, c) \) \( (1,2,1) ;(2,4,2) ;(1,4,4) ;(4,4,1) ;(3,6,3) ; \)…
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