Let S={1, 2, 3, ldots, 100}. Suppose b and c | vedclass

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(A) The quadratic equation $4x^2+bx+c=0$ has equal roots if its discriminant $D = b^2 - 4(4)(c) = 0$. This implies $b^2 = 16c$,or $b^2 = (4\sqrt{c})^2

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$0.001$

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(A) The quadratic equation $4x^2+bx+c=0$ has equal roots if its discriminant $D = b^2 - 4(4)(c) = 0$. This implies $b^2 = 16c$,or $b^2 = (4\sqrt{c})^2$,which means $b = 4\sqrt{c}$. Since $b$ must be an integer and $b \in S$,$c$ must be a perfect square such that $4\sqrt{c} \in \{1, 2, \ldots, 100\}$. Let $c = k^2$ for some integer $k$. Then $b = 4k$. Since $1 \le b \le 100$,we have $1 \le 4k \le 100$,which implies $1 \le k \le 25$. Also,$c = k^2$ must be in $S$,so $1 \le k^2 \le 100$,which implies $1 \le k \le 10$. Thus,the possible values for $k$ are $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$. There are $10$ such pairs $(b, c)$. The total number of ways to choose $b$ and $c$ from $S$ is $100 	imes 100 = 10000$. The probability is $\frac{10}{10000} = \frac{1}{1000} = 0.001$.

Let $S=\{1, 2, 3, \ldots, 100\}$. Suppose $b$ and $c$ are chosen at random from the set $S$. The probability that $4x^2+bx+c=0$ has equal roots is

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