If the roots of the quadratic equation x2-4x-log3a=0 are real, then the least value of a is

Question

If the roots of the quadratic equation x2-4x-log3a=0 are real, then the least value of a is (A) 81 (B) 1/81 (C) 1/64 (D) None of these

Tardigrade Admin · Accepted Answer

Since, the roots of the given equation are real. ∴ Disc>0⇒ 16+4 text log3a ge 0 ⇒ log 3a ge -4⇒ a ge 3-4⇒ a ge 1/81 Hence, the least value of a is 1/81 .

Q. If the roots of the quadratic equation $x^{2} - 4 x - l o g_{3} a = 0$ are real, then the least value of a is

81

1/81

1/64

None of these

Since, the roots of the given equation are real. $∴$ $D i sc > 0 \Rightarrow 16 + 4 l o g_{3} a \geq 0$ $\Rightarrow$ $lo g_{3} a \geq - 4 \Rightarrow a \geq 3^{- 4} \Rightarrow a \geq 1/81$ Hence, the least value of a is $1/81$ .

Q. If the roots of the quadratic equation x2−4x−log3​a=0 are real, then the least value of a is

81

1/81

1/64

None of these

Since, the roots of the given equation are real. ∴ Disc>0⇒16+4log3​a≥0 ⇒ log3​a≥−4⇒a≥3−4⇒a≥1/81 Hence, the least value of a is 1/81 .

Q. If the roots of the quadratic equation $x^{2} - 4 x - l o g_{3} a = 0$ are real, then the least value of a is

Since, the roots of the given equation are real. $∴$ $D i sc > 0 \Rightarrow 16 + 4 l o g_{3} a \geq 0$ $\Rightarrow$ $lo g_{3} a \geq - 4 \Rightarrow a \geq 3^{- 4} \Rightarrow a \geq 1/81$ Hence, the least value of a is $1/81$ .