TS EAMCET · Maths · Quadratic Equation

The sum of all distinct roots of the equation $x^5-3 x^4+5 x^3-5 x^2+3 x-1=0$ is

A 1
B 2
C 3
D $2 \sqrt{3}$

Verified Solution

Answer & Solution

Correct Answer

(B) 2

Step-by-step Solution

Detailed explanation

No solution. Refer to answer key.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

If $x=9$ is a chord of contact of the hyperbola $x^2-y^2=9$, then the equation of the tangent at one of the points of contact is

TS EAMCET 2013 Medium
If $x=\log \left(y+\sqrt{y^2+1}\right)$ then $y=$

TS EAMCET 2023 Medium
A person who tosses an unbiased coin gains two points for turning up a head and loses one point for a tail. If three coins are tossed and the total score $X$ is observed, then the range of $x$ is

TS EAMCET 2004 Hard
If $\mathrm{I}_1=\int \sin ^6 x d x$ and $\mathrm{I}_2=\int \cos ^6 x d x$ then $\mathrm{I}_1+\mathrm{I}_2=$

TS EAMCET 2025 Medium
In a triangle ABC , if $r_1 r_2+r_3=35, r_2 r_3+m_1=63$ and $r_3 r_1+r r_2=45$, then $2 s=$

TS EAMCET 2024 Medium
If $A$ and $B$ are events of a random experiment such that $P(A \cup B)=\frac{4}{5}, P(\bar{A} \cup \bar{B})=\frac{7}{10}$ and $P(B)=\frac{2}{5}$, then $P(A)$ equals

TS EAMCET 2009 Easy

Explore more questions on app

From TS EAMCET

Match the entries in List I with those in List II.

TS EAMCET 2018 Easy
A car moving towards a cliff emits sound of frequency ' $n$ '. If the difference in frequencies of the horn and its echo heard by the driver of the car is $10 \%$ of ' $n$ ', then the speed of the car is nearly (Speed of sound in air is $336 \mathrm{~ms}^{-1}$ )

TS EAMCET 2025 Medium
$\int \frac{(1 - \cos x)^{2 / 7}}{(1 + \cos x)^{9 / 7}} d x =$

TS EAMCET 2021 Medium
Match the functions of List-I with their nature in List-II and choose the correct option.
Then the correct match is

TS EAMCET 2019 Easy
Match the following Reactants (A) $\mathrm{C}_2 \mathrm{H}_5 \mathrm{Cl}$, moist $\mathrm{Ag}_2 \mathrm{O}$ (B) $\mathrm{C}_2 \mathrm{H}_5 \mathrm{Cl}$, aqueous ethanolic $\mathrm{AgCN}$ Products (i) $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{ONO}$ (ii) $\mathrm{C}_2 \mathrm{H}_4$ aqueous (iii) $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OH}$ ethanolic $\mathrm{AgNO}_2$ (D) $\mathrm{C}_2 \mathrm{H}_5 \mathrm{Cl}$, ethanolic (iv) $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{NC}$ $\mathrm{KOH}$ (v) $\mathrm{C}_2 \mathrm{H}_6$ The correct match is

TS EAMCET 2007 Medium
A thermocol box has a total wall area (including the lid) of $1.0 \mathrm{~m}^2$ and wall thickness of $3 \mathrm{~cm}$. It is filled with ice at $0^{\circ} \mathrm{C}$. If the average temperature outside the box is $30^{\circ} \mathrm{C}$ throughout the day, the amount of ice that melts in one day is \[ \begin{aligned} & \text { IUse } K_{\text {thermosol }}=0.03 \mathrm{~W} / \mathrm{mK}, \ & L_{\text {fusion (ire) }}=3.00 \times 10^5 \mathrm{~J} / \mathrm{kg} \text { ] } \end{aligned} \]

TS EAMCET 2017 Hard

Explore more questions on app

The sum of all distinct roots of the equation \(x^5-3 x^4+5 x^3-5 x^2+3 x-1=0\) is

Answer & Solution

Step-by-step Solution

See the Complete Solution