MCQ
If the sum of the roots of the equation $\text{x}^2-\text{x}=\lambda(2\text{x}-1)$ is zero, then $\lambda=$
- A$-2$
- B$2$
- ✓$-\frac{1}{2}$
- D$\frac{1}{2}$
✓
Answer
Correct option: C.
$-\frac{1}{2}$
$\Rightarrow\text{x}^2-\text{x}=\lambda(2\text{x}-1)$
$\Rightarrow\text{x}^2-\text{x}=2\lambda\text{x}-\lambda$
$\Rightarrow\text{x}^2-\text{x}-2\lambda\text{x}+\lambda=0$
$\Rightarrow\text{x}^2-(1+2\lambda)\text{x}+\lambda=0$
Sum of roots $=\frac{-\text{b}}{\text{a}}$
$=\frac{1+2\lambda}{1}$
$\frac{1+2\lambda}{1}=0$
$\Rightarrow2\lambda=-1$
$\lambda=-\frac{1}{2}$
$\Rightarrow\text{x}^2-\text{x}=2\lambda\text{x}-\lambda$
$\Rightarrow\text{x}^2-\text{x}-2\lambda\text{x}+\lambda=0$
$\Rightarrow\text{x}^2-(1+2\lambda)\text{x}+\lambda=0$
Sum of roots $=\frac{-\text{b}}{\text{a}}$
$=\frac{1+2\lambda}{1}$
$\frac{1+2\lambda}{1}=0$
$\Rightarrow2\lambda=-1$
$\lambda=-\frac{1}{2}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If diameter of a semicircle is 35 cm. Find its length.
$\triangle\text{ABC}\sim\triangle\text{DEF}.$ If $BC = 3\ cm, EF = 4\ cm$ and $\text{ar}(\triangle\text{ABC})=54\text{cm}^2,$ then $\text{ar}(\triangle\text{DEF}):$
→From a point $Q$, the length of the tangent to a circle is $24\ cm$ and the distance of $Q$ from the centre is $25\ cm$. The radius of the circle is:
→The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after:
→In the given figure, if $\text{AD, AE}$ and $\text{BC}$ are tangents to the circle at $\text{D, E}$ and $\text{F}$ respectively, Then:
→ΔABC and ΔDEF are equilateral triangles, A(ΔABC) : A(ΔDEF) = 1 : 2. If AB = 4 then what is length of DE?
Mark the correct alternative in the following:
If the sum of $n$ terms of an $A.P.$ is $2n^2 + 5n$, then its $n^{th}$ term is:
→If the sum of $n$ terms of an $A.P.$ is $2n^2 + 5n$, then its $n^{th}$ term is:
If $16\cot x=12,$ then $\frac{\sin\text{x}-\cos\text{x}}{\sin\text{x}+\cos\text{x}} $ equals:
→How many bags of grain can be stored in a cuboidal granary $(8m \times 6m \times 3m),$ if each bag occupies a space of $0.64m^3$?
→If $(\sec \theta-1)(\sec \theta+1)=\frac{1}{3}$, then $\cos \theta=$ _____
→