The values of alpha, for which left|begin{arr | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\left|\begin{array}{ccc}1 & \frac{3}{2} & \alpha+\frac{3}{2} \ 1 & \frac{1}{3} & \alpha+\frac{1}{3} \ 2 \alpha+3 & 3 \alpha+1 &

Vedclass · Accepted Answer

$(-3,0)$

Vedclass · Answer

$\left|\begin{array}{ccc}1 & \frac{3}{2} & \alpha+\frac{3}{2} \ 1 & \frac{1}{3} & \alpha+\frac{1}{3} \ 2 \alpha+3 & 3 \alpha+1 & 0\end{array}ight|=0$

$ \Rightarrow(2 \alpha+3)\left\{\frac{7 \alpha}{6}ight\}-(3 \alpha+1)\left\{\frac{-7}{6}ight\}=0 $

$ \Rightarrow(2 \alpha+3) \cdot \frac{7 \alpha}{6}+(3 \alpha+1) \cdot \frac{7}{6}=0 $

$ \Rightarrow 2 \alpha^2+3 \alpha+3 \alpha+1=0 $

$ \Rightarrow 2 \alpha^2+6 \alpha+1=0 $

$ \Rightarrow \alpha=\frac{-3+\sqrt{7}}{2}, \frac{-3-\sqrt{7}}{2}$

Hence option $(2)$ is correct.

The values of $\alpha$, for which $\left|\begin{array}{ccc}1 & \frac{3}{2} & \alpha+\frac{3}{2} \\ 1 & \frac{1}{3} & \alpha+\frac{1}{3} \\ 2 \alpha+3 & 3 \alpha+1 & 0\end{array}\right|=0$, lie in the interval

Similar Questions

If $A = \left| {\,\begin{array}{*{20}{c}}{\sin (\theta + \alpha )}&{\cos (\theta + \alpha )}&1\\{\sin (\theta + \beta )}&{\cos (\theta + \beta )}&1\\{\sin (\theta + \gamma )}&{\cos (\theta + \gamma )}&1\end{array}\,} \right|$ ,then

Evaluate the determinants

$\left|\begin{array}{ccc}2 & -1 & -2 \\ 0 & 2 & -1 \\ 3 & -5 & 0\end{array}\right|$

The value of $'a'$ for which the system of equation $a^3x + (a + 1)^3y + (a + 2)^3 z = 0$ ; $ax + (a + 1)y + (a + 2)z = 0$ ; $x + y + z = 0$ has a non-zero solution is :-

If $D_1$ and $D_2$ are two $3 \times 3$ diagonal matrices, then

$\left| {\,\begin{array}{*{20}{c}}0&{p - q}&{p - r}\\{q - p}&0&{q - r}\\{r - p}&{r - q}&0\end{array}\,} \right| = $