If the roots of the given equation 2 x^2 + 3( - 2)x + + 4 = 0 be … - Vidyadip

MCQ

If the roots of the given equation $2{x^2} + 3(\lambda - 2)x + \lambda + 4 = 0$ be equal in magnitude but opposite in sign, then $\lambda $=

A
$1$
✓
$2$
C
$3$
D
$2/3$

✓

Answer

Correct option: B.

$2$

b
(b) Let roots are $\alpha $and $ - \alpha $, then sum of the roots

$\alpha + ( - \alpha ) = \frac{{3(\lambda - 2)}}{2}$

$\Rightarrow 0 = \frac{3}{2}(\lambda - 2)$

==>$\lambda = 2$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Consider the family of lines $x(a + b) + y = 1,$ where $a, b$ and $c$ are the roots of the equation $x^3 -3x^2 + x + \lambda= 0$ such that $c \in [1,2] .$ If the given family of lines makes triangle of area $'A'$ with coordinate axis, then maximum value of $'A'$ (in sq. units) will be -

Let $S=\{z \in C :|z-3| \leq 1$ and $z(4+3 i)+\bar{z}(4-3 i) \leq 24\}$.

If $\alpha+i \beta$ is the point in $S$ which is closest to $4 i$, then $25(\alpha+\beta)$ is equal to

The ratio of the sums of first $n$ even numbers and $n$ odd numbers will be

If the eccentricity of an ellipse be $1/\sqrt 2 $, then its latus rectum is equal to its

The chances of throwing a total of $3$ or $5$ or $11$ with two dice is

The length of the tangent from the point $(4, 5)$ to the circle ${x^2} + {y^2} + 2x - 6y = 6$ is

The magnitude of the gradient of the tangent at an extremity of latera recta of the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1$ is equal to (where $e$ is the eccentricity of the hyperbola)

The period of the function $\sin \left( {\frac{{\pi x}}{2}} \right) + \cos \left( {\frac{{\pi x}}{2}} \right)$ is

If the function $f(x)=\frac{1}{x} \log _{e}(\frac{1+\frac{x}{a}}{1-\frac{x}{b}}) , \quad x<0$

$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad k \quad, \quad x=0$

$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\frac{\cos ^{2} x-\sin ^{2} x-1}{\sqrt{x^{2}+1}-1} ,\,\,\, x>0$

is continuous at $x=0$, then $\frac{1}{a}+\frac{1}{b}+\frac{4}{k}$ is equal to :

Let $g(x) = | |x + 2| -3|$ . If $'a'$ denotes the number of relative minima, $'b'$ denotes the number of relative maxima and $'c'$ denotes the product of the zeroes of $g(x)$ , then the value of $(a + 2b -c)$ is