The probability of choosing randomly a number | vedclass

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(D) The given quadratic equation is $x^2 + 4x + c = 0$. For the roots to be real,the discriminant $D$ must be greater than or equal to $0$. $D = b^2 -

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$\frac{4}{9}$

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(D) The given quadratic equation is $x^2 + 4x + c = 0$. For the roots to be real,the discriminant $D$ must be greater than or equal to $0$. $D = b^2 - 4ac \geq 0$ Substituting $a = 1$,$b = 4$,we get: $4^2 - 4(1)(c) \geq 0$ $16 - 4c \geq 0$ $16 \geq 4c$ $c \leq 4$. Since $c$ is chosen from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$,the possible values for $c$ are $\{1, 2, 3, 4\}$. There are $4$ favorable outcomes out of $9$ total outcomes. Therefore,the required probability is $\frac{4}{9}$.

The probability of choosing randomly a number $c$ from the set $\{1, 2, 3, \ldots, 9\}$ such that the quadratic equation $x^2 + 4x + c = 0$ has real roots is

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