The possible value(s) of $a$ for which the equation $x^{2} + 2 x - (a^{3} - 3 a - 3) = 0$ has real roots is/are

4

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

6

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

2

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

- 1

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

Open in App

Solution

The correct option is D $- 1$
$x^{2} + 2 x - (a^{3} - 3 a - 3) = 0$
For real roots,
$D \geq 0$
$\Rightarrow 4 + 4 (a^{3} - 3 a - 3) \geq 0 \Rightarrow 1 + a^{3} - 3 a - 3 \geq 0 \Rightarrow a^{3} - 3 a - 2 \geq 0 \Rightarrow (a + 1) (a^{2} - a - 2) \geq 0 \Rightarrow (a + 1)^{2} (a - 2) \geq 0$
$∴ a \in {- 1} \cup [2, \infty)$

Suggest Corrections

Similar questions

a

x^{2} + 2 x - (a^{3} - 3 a - 3) = 0

a

x^{2} + 2 x - (a^{3} - 3 a - 3) = 0

a

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

{(\frac{x}{1 + x^{2}})}^{2} + a (\frac{x}{1 + x^{2}}) + 3 = 0

a

(- \infty, - λ) \cup (μ, \infty)

\frac{λ + μ}{13}

a

x^{2} + a x + 16 = 0

Join BYJU'S Learning Program