Question

Let `head` means 1 and `tail` means 2 and coefficients of the equation $a{x}^2+bx+c=0$ are chosen by tossing a fair coin. The probability that the roots of the equation are non-real, is equal to

• A. $\frac{5}{8}$
• B. $\frac{7}{8}$
• C. $\frac{3}{8}$
• D. $\frac{1}{8}$

Answer 1

The correct option is B $\frac{7}{8}$

a, b, c may be 1 or 2
$a{x}^2+bx+c=0$ has non-real roots if $b^2-4ac<0$
$\begin{array}{ccc}b& 1& 2\\ (a,c)& (1,1),(1,2),(2,1),(2,2)& (1,2),(2,1)(2,2)\end{array}=7$
Hence required probabilidy $=\frac{7}{2^3}=\frac{7}{8}.$