Question 19

Mathematics Linear and Quadratic Equations Medium

Coefficients of quadratic equation \(a x^{2}+b x+c=0\) are chosen by tossing three fair coins where 'head' means one and 'tail' means two. Then the probability that roots of the equation are imaginary is

(A) \(\frac{7}{8}\)
(B) \(\frac{5}{8}\)
(C) \(\frac{3}{8}\)
(D) \(\frac{1}{8}\)
✓ Correct Answer: Option A Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

Total number of cases is 8. \[\] \(a, b, c\) can take values 1 and 2 only. The roots are real when \(b=2, a\) and \(c\) are 1,1 . \[\] Required probability \(=1-\frac{1}{8}=\frac{7}{8}\). \[\] Choice (A)

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