If the roots of the quadratic equation x^2 - | vedclass

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(B) For the quadratic equation $x^2 - 4x - \log_3 a = 0$ to have real roots,the discriminant $D$ must be greater than or equal to $0$.The discriminant

Vedclass · Accepted Answer

$1/81$

Vedclass · Answer

(B) For the quadratic equation $x^2 - 4x - \log_3 a = 0$ to have real roots,the discriminant $D$ must be greater than or equal to $0$.The discriminant $D$ is given by $b^2 - 4ac$.Here,$a = 1$,$b = -4$,and $c = -\log_3 a$.$D = (-4)^2 - 4(1)(-\log_3 a) \geq 0$$16 + 4\log_3 a \geq 0$$4\log_3 a \geq -16$$\log_3 a \geq -4$Since the base $3 > 1$,the inequality direction remains the same:$a \geq 3^{-4}$$a \geq \frac{1}{81}$Thus,the minimum value of $a$ is $\frac{1}{81}$.

If the roots of the quadratic equation $x^2 - 4x - \log_3 a = 0$ are real,then what is the minimum value of $a$?

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