COMEDK · Maths · 36. Probability
The coefficients \(a, b\) and \(c\) of the quadratic equation, \(a x^{2}+b x+c=0\) are obtained by throwing a dice three times. The probability that this equation has equal roots is
- A \(\dfrac{1}{72}\)
- B \(\dfrac{5}{216}\)
- C \(\dfrac{1}{36}\)
- D \(\dfrac{1}{54}\)
Answer & Solution
Correct Answer
(B) \(\dfrac{5}{216}\)
Step-by-step Solution
Detailed explanation
The quadratic equation \(ax^{2} + bx + c = 0\) has equal roots if the discriminant \(D = b^{2} - 4ac = 0\), which implies \(b^{2} = 4ac\). Since \(a, b, c\) are outcomes of throwing a dice three times, \(a, b, c \in \{1, 2, 3, 4, 5, 6\}\). The total number of possible outcomes…
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