The least value of $a$ for which roots of the equation $x^{2} - 2 x - {log}_{4} a = 0$ are real is

\frac{1}{16}

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\frac{1}{4}

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4

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Solution

The correct option is B $\frac{1}{4}$
The given equation $x^{2} - 2 x - l o g_{4} a = 0$
$\Rightarrow$ For real roots, $D \geq 0$
$\Rightarrow 4 + 4 {log}_{4} a \geq 0$
$\Rightarrow {log}_{4} a \geq - 1$
$\Rightarrow a \geq 4^{- 1} \Rightarrow a \geq \frac{1}{4}$

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The least value of a for which roots of the equation x2−2x−log4a=0 are real is

The correct option is B 14The given equation x2−2x−log4a=0⇒ For real roots, D≥0⇒4+4log4a≥0⇒log4a≥−1⇒a≥4−1⇒a≥14

The least value of $a$ for which roots of the equation $x^{2} - 2 x - {log}_{4} a = 0$ are real is

The correct option is B $\frac{1}{4}$
The given equation $x^{2} - 2 x - l o g_{4} a = 0$
$\Rightarrow$ For real roots, $D \geq 0$
$\Rightarrow 4 + 4 {log}_{4} a \geq 0$
$\Rightarrow {log}_{4} a \geq - 1$
$\Rightarrow a \geq 4^{- 1} \Rightarrow a \geq \frac{1}{4}$