MCQ
If the equation $4x^2- 3kx + 1 = 0$ has equal roots then $k = ?$
- A$\pm\frac{2}{3}$
- B$\pm\frac{1}{3}$
- C$\pm\frac{3}{4}$
- ✓$\pm\frac{4}{3}$
✓
Answer
Correct option: D.
$\pm\frac{4}{3}$
Since the roots of the equation $4 {x}^2-3 {kx}+1=0$ are equal,
$D = 0$
$\Rightarrow b^2-4 a c=0$
$\Rightarrow(-3 k)^2-4 \times 4 \times 1=0$
$\Rightarrow 9 k^2-16=0$
$\Rightarrow 9 k^2=16$
$\Rightarrow\text{k}^2=\frac{16}{9}$
$\Rightarrow\text{k}=\pm\frac{4}{3}$
$D = 0$
$\Rightarrow b^2-4 a c=0$
$\Rightarrow(-3 k)^2-4 \times 4 \times 1=0$
$\Rightarrow 9 k^2-16=0$
$\Rightarrow 9 k^2=16$
$\Rightarrow\text{k}^2=\frac{16}{9}$
$\Rightarrow\text{k}=\pm\frac{4}{3}$
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
A number is selected at random from the numbers $1$ to $30$. The probability that it is a prime number is :
→A bag contains cards numbered from 1 to 25. A card is drawn at random from the bag. The probability that the number on this card is divisible by both 2 and 3 is:
In figure, AT is a tangent to the circle with centre O such that OT = 4cm and $\angle\text{OTA}=30^\circ.$ Then AT is equal to:
→If two perpendicular tangents $P A$ and $P B$ are drawn from an external point to a circle of radius 4 cm , then the length of each tangent is
→The maximum volume of a cone that can be carved out of a solid hemisphere of radius $r$ is :
→The value of $\cot 10^{\circ} \cot 15^{\circ} \cot 75^{\circ} \cot 80^{\circ}$ is equal to:
→The area of the triangle formed by the line $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}} =1$ with the co $-$ ordinate axis is :
→If $P(A)$ denotes the probability of an event $A$, then
→$(\operatorname{cosec} \theta-\sin \theta)(\sec \theta-\cos \theta)(\tan \theta+\cot \theta)$ is equal
→A dice is rolled twice. The probability that 5 will not come up either time is