If each of the coefficients $a, b, c$ in the equation $a x^2+b x$ $+c=0$ is determined by throwing a die, then the probability that the equation will have equal roots, is

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Aicharya · Accepted Answer

$a x^2+b x+c=0$
For equal roots, $b^2=4 a c$ $\begin{array}{|c|c|c|} \hline \mathbf{b} & (\mathbf{a}, \mathbf{c}) & \text { Total } \\ \hline 1 & - & 0 \\ \hline 2 & (1,1) & 1 \\ \hline 3 & - & 0 \\ \hline 4 & (1,4)(4,1)(2,2) & 3 \\ \hline 5 & - & 0 \\ \hline 6 & (3,3) & 1 \\ \hline \end{array}$ Required probability $=\frac{5}{216}$

If each of the coefficients $a, b, c$ in the equation $a x^2+b x$ $+c=0$ is determined by throwing a die,…

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