The set of values of $a$ for which $x^{2} + a x + {sin}^{- 1} (x^{2} - 4 x + 5) + {cos}^{- 1} (x^{2} - 4 x + 5) = 0$ has at least one solution is

(- \infty, - \sqrt{2 π}] \cup - [\sqrt{2 π}, \infty)

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

(- \infty, - \sqrt{2 π}) \cup (\sqrt{2 π}, \infty)

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

R

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

n o n e o f t h e s e

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

Open in App

Solution

The correct option is C $(- \infty, - \sqrt{2 π}) \cup (\sqrt{2 π}, \infty)$
We have,
$\begin{matrix} x^{2} + a x + {sin}^{- 1} (x^{2} - 4 x + 5) + {cos}^{- 1} (x^{2} - 4 x + 5) = 0 x^{2} + a x + \frac{π}{2} = 0 \end{matrix}$

For at least one solution
$\begin{matrix} x^{2} + a x + {sin}^{- 1} (x^{2} - 4 x + 5) + {cos}^{- 1} (x^{2} - 4 x + 5) = 0 x^{2} + a x + \frac{π}{2} = 0 D \geq 0 (a^{2} - 4. \frac{π}{2}) \geq 0 (a^{2} - 2 π) \geq 0 a^{2} \geq 2 π (a + 2 \sqrt{2 π}) (a - 2 \sqrt{2 π}) \geq 0 + - + - ------------------------ - - \sqrt{2 π} \sqrt{2 π} a t (- \infty, - \sqrt{2 π}) \cup (\sqrt{2 π}, \infty) \end{matrix}$

Option $B$ is correct answer.

Suggest Corrections

Similar questions

Q. The set of value(s) of

a

for which

x^{2} + a x + {sin}^{- 1} (x^{2} - 4 x + 5) + {cos}^{- 1} (x^{2} - 4 x + 5) = 0

has at least one solution is

Q. The value of a for which

x^{2} + a x + {s i n}^{- 1} (x^{2} - 4 x + 5) + {c o s}^{- 1} (x^{2} - 4 x + 5) = 0

has at least one solution is

The value of $a = - λ - \frac{π}{μ}$ , such that $x^{2} + a x + s i n^{- 1} (x^{2} - 4 x + 5) + c o s^{- 1} (x^{2} - 4 x + 5) = 0$ has atleast one solution. Then $λ + μ$ is equal to

Q. Solve:

{cos}^{- 1} (\frac{x^{2} - 1}{x^{2} + 1}) + {tan}^{- 1} \frac{2 x}{x^{2} - 1} = \frac{2 π}{3}

Q. Solve the equation:

{cos}^{- 1} (\frac{x^{2} - 1}{x^{2} + 1}) + {sin}^{- 1} (\frac{2 x}{x^{2} + 1}) + {tan}^{- 1} (\frac{2 x}{x^{2} - 1}) = \frac{2 π}{3}

Join BYJU'S Learning Program

The set of values of a for which x2+ax+sin−1(x2−4x+5)+cos−1(x2−4x+5)=0 has at least one solution is

The set of values of $a$ for which $x^{2} + a x + {sin}^{- 1} (x^{2} - 4 x + 5) + {cos}^{- 1} (x^{2} - 4 x + 5) = 0$ has at least one solution is