If the equation 5 x2-10 x-log 1-5 a-0 has real roots then the minimum value of a isA- none of theseB- 1-1010C- 1-510D- 1-55

The correct option is D Solution : 5x^2 10x+log_1/5a=0 has real roots. 100 20 log_1/5a≥ 0 log _1/5a≤ 5 = log_1/5(1/5)^5 a≥ 0 and a≥1/5^5 minimum value of a=1/ ...

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Byju's Answer

Standard XII

Mathematics

Discriminant

If the equati...

Question

If the equation $5 x^{2} - 10 x + l o g_{\frac{1}{5}} a = 0$ has real roots then the minimum value of a is

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Solution

The correct option is A
$S o l u t i o n : 5 x^{2} - 10 x + l o g_{\frac{1}{5}} a = 0$ has real roots.
$100 - 20 l o g_{\frac{1}{5}} a \geq 0$
$l o g_{\frac{1}{5}} a \leq 5 = l o g_{\frac{1}{5}} {(\frac{1}{5})}^{5}$
$a \geq 0$ and $a \geq \frac{1}{5^{5}}$
minimum value of $a = \frac{1}{5^{5}}$

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If the equation 5x2−10x+log15a=0 has real roots then the minimum value of a is

The correct option is A Solution : 5x2−10x+log15a=0 has real roots. 100−20log15a≥0 log15a≤5=log15(15)5 a≥0 and a≥155 minimum value of a=155

If the equation $5 x^{2} - 10 x + l o g_{\frac{1}{5}} a = 0$ has real roots then the minimum value of a is

The correct option is A
$S o l u t i o n : 5 x^{2} - 10 x + l o g_{\frac{1}{5}} a = 0$ has real roots.
$100 - 20 l o g_{\frac{1}{5}} a \geq 0$
$l o g_{\frac{1}{5}} a \leq 5 = l o g_{\frac{1}{5}} {(\frac{1}{5})}^{5}$
$a \geq 0$ and $a \geq \frac{1}{5^{5}}$
minimum value of $a = \frac{1}{5^{5}}$