The value of x obtained from the equation | , * 20 c x + & & & x … - Vidyadip

MCQ

The value of $x$ obtained from the equation $\left| {\,\begin{array}{*{20}{c}}{x + \alpha }&\beta &\gamma \\\gamma &{x + \beta }&\alpha \\\alpha &\beta &{x + \gamma }\end{array}\,} \right| = 0$ will be

✓
$0 $ and $ - (\alpha + \beta + \gamma )$
B
$0$ and $(\alpha + \beta + \gamma )$
C
$1$ and $(\alpha - \beta - \gamma )$
D
$0 $ and $({\alpha ^2} + {\beta ^2} + {\gamma ^2})$

✓

Answer

Correct option: A.

$0 $ and $ - (\alpha + \beta + \gamma )$

a
(a) Equation given, $\left| {\,\begin{array}{*{20}{c}}{x + \alpha + \beta + \gamma }&\beta &\gamma \\{x + \alpha + \beta + \gamma }&{x + \beta }&\alpha \\{x + \alpha + \beta + \gamma }&\beta &{x + \gamma }\end{array}\,} \right| = 0$,

$[{C_1} \to {C_1} + ({C_2} + {C_3})]$

or $(x + \alpha + \beta + \gamma )\,\left| {\,\begin{array}{*{20}{c}}1&\beta &\gamma \\1&{x + \beta }&\alpha \\1&\beta &{x + \gamma }\end{array}\,\,} \right|\, = 0$

or $(x + \alpha + \beta + \gamma )\,\left| {\,\begin{array}{*{20}{c}}1&\beta &\gamma \\0&x&{\alpha - \gamma }\\0&0&x\end{array}\,} \right|\, = \,0$,

$\left[ \begin{array}{l}{R_2} \to {R_2} - {R_1}\\{R_3} \to {R_3} - {R_1}\end{array} \right]$

or $(x + \alpha + \beta + \gamma )[{x^2} - 0] = 0$

or ${x^2}(x + \alpha + \beta + \gamma ) = 0$

$\therefore $ $x = 0$ or $x = - (\alpha + \beta + \gamma )$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The value of $\int_0^{{{\sin }^2}x} {{{\sin }^{ - 1}}\sqrt t \,dt + \int_0^{{{\cos }^2}x} {{{\cos }^{ - 1}}\sqrt t \,dt} } $ is

If $O $ be the origin and the position vector of $A$ be $4\,i + 5\,j,$ then a unit vector parallel to $\overrightarrow {OA} $ is

Let $\vec{a}$ and $\vec{b}$ are non-collinear. If $\vec{c}=(x-2) \vec{a}+\vec{b}$ and $\vec{d}=(2 x+1) \vec{a}-\vec{b}$ are collinear, then find the value of $x$.

The complete set of values of $x$ in which $f(x) = 2 \log_e(x -2) -x^2 + 4x + 1$ increases, is :-

If $X$ is a random variable with probability distribution as given below :

$X = x_i$	$0$	$1$	$2$	$3$
$P(X = X_i)$	$k$	$3k$	$3k$	$k$

The value of $k$ and its variance are :

If x, y, z are non-zero real numbers, then the inverse, then the inverse of the matrix $\begin{bmatrix}\text{x} & 0 & 0\\ 0 & \text{y} & 0 \\ 0 & 0 & \text{z}\end{bmatrix}$, is:

For which of the following element in the determinant $\triangle=\begin{bmatrix}5&-5&8\\6&2&-1\\5&-6&8\end{bmatrix},$ the minor and the cofactor both are zero.

$\int_{}^{} {{{\sin }^2}x\cos x\;dx} $ is equal to

A die is rolled. Let $A$ be event of getting number more than 3 and B be event of getting number less than 5 . Then value of $P ( A \cup B )$ :

he two curves $x^3 - 3xy^2 + 2 = 0$ and $3x^2y - y^3 - 2 = 0$ intersect at an angle of: