If the equations x^2+2x+3 =0 and 2x^2+3x+5 =0 have a non-zero com… - Vidyadip

MCQ

If the equations $\text{x}^2+2\text{x}+3\lambda=0$ and $2\text{x}^2+3\text{x}+5\lambda=0$ have a non-zero common roots, then $\lambda=$

A
1
✓
-1
C
3
D
None of these.

✓

Answer

Correct option: B.

-1

Let a be the common roots of the equations $\text{x}^2+2\text{x}+3\lambda=0$ and $2\text{x}^2+3\text{x}+5\lambda=0$
Therefore
$\alpha^2+2\text{a}+3\lambda=0\ ...(1)$
$2\alpha^2+3\alpha+5\lambda=0\ ...(2)$
Solving (1) and (2) by cross multiplication, we get
$\frac{\alpha^2}{10\lambda-9\lambda}=\frac{\alpha}{6\lambda-5\lambda}=\frac{1}{3-4}$
$\Rightarrow\text{a}^2=-\lambda,\alpha=-\lambda$
$\Rightarrow-\lambda=\lambda^2$
$\Rightarrow\lambda=-1$

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 "MCQ" from COMPLEX NUMBERS AND QUADRATIC EQUATIONS→COMPLEX NUMBERS AND QUADRATIC EQUATIONS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of exactly 3 girls:

The complex number z which satisfies the condition $\Big|\frac{\text{i}+\text{z}}{\text{i}-\text{z}}\Big|=1$ lies on:

$\alpha$, $\beta$ ,$\gamma$ are roots of equatiuon $x^3 -x -1 = 0$ then equation whose roots are $\frac{1}{{\beta + \gamma }},\frac{1}{{\gamma + \alpha }},\frac{1}{{\alpha + \beta }}$ is

Let e denote the base of the natural logarithm. The value of the real number a for which the right hand limit

$\lim _{x \rightarrow 0^{+}} \frac{(1-x)^{\frac{1}{x}}-e^{-1}}{x^a}$

is equal to a nonzero real number, is. . . . . . .

On the occasion of Deepawali festival, each student of a class sends greeting cards to the others.If there are 20 students in the class, then the total number of greeting cards exchanged by the students is:

$\frac{{1 - 2i}}{{2 + i}} + \frac{{4 - i}}{{3 + 2i}} = $

The equation of the line with slope $-\frac{3}{2}$ and which is concurrent with the lines 4x + 3y - 7 = 0 and 8x + 5y - 1 = 0 is:

On the ellipse $\frac{{{x^2}}}{{18}} + \frac{{{y^2}}}{8} = 1$ the point $M$ nearest to the line $2x - 3y + 25 = 0$ is

Two tangent lines $l_{1}$ and $l_{2}$ are drawn from the point $(2,0)$ to the parabola $2 y^{2}=-x$. If the lines $l_{1}$ and $l_{2}$ are also tangent to the circle $(x-5)^{2}+y^{2}=r$, then $17 r$ is equal to.

The centre of a regular polygon of $n$ sides is located at the point $z = 0$ and one of its vertex ${z_1}$ is known. If ${z_2}$ be the vertex adjacent to ${z_1}$, then ${z_2}$ is equal to