If the roots of the quadratic equation $x^{2} - 2 x - {log}_{2} A = 0$ are real, then the least value of $A$ is

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{1}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{1}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $\frac{1}{2}$
Given $x^{2} - 2 x - {log}_{2} A = 0$
Roots are real if $△ \geq 0$
$△ = 4 + 4 {log}_{2} A \geq 0$
$1 + {log}_{2} A \geq 0$
$A > \frac{1}{2}$
So the least value is $A = \frac{1}{2}$

Suggest Corrections

Similar questions

x^{2} - 4 x - {log}_{3} a = 0

a

The roots of a quadratic equation $x^{2} - 4 x - {log}_{3} a = 0$ are real. Then what is the least value of $a$ ?

If α,β are the roots of the quadratic equation $x^{2}$ – (a – 2)x –(a+1) =0, where 'a' is a variable then the least value of $α^{2}$ + $β^{2}$

The roots of a quadratic equation $x^{2} - 4 x - a = 0$ are real. Then what is the least value of $a$ ?

If $x^{2}$ +px + q = 0 is the quadratic equation whose roots are a – 2 and b – 2 where a and b are the roots of $x^{2}$ - 3x + 1 =0, then

Join BYJU'S Learning Program