TS EAMCET · Maths · Quadratic Equation
\(p\) is non-zero real number. If the equation whose roots are the squares of the roots of the equation \(x^3-p x^2+p x-1=0\) is identical with the given equation, then \(p=\)
- A \(\frac{1}{2}\)
- B 2
- C 3
- D -1
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
Let \(\alpha, \beta, \gamma\) are roots of equation \(x^3-p x^2+p x-1=0\) \(\because \quad \alpha+\beta+\gamma=p\) \(\alpha \beta+\beta \gamma+\alpha \gamma=p\) \(\alpha \beta \gamma=1\) Also given, \(\quad \alpha^2+\beta^2+\gamma^2=p\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \([A]_{3 \times 3}\) be a non-singular matrix such that \(A^{-1}=\frac{1}{3}\left(A^2-5 A+7 I\right)\).
Then \(17 A^8-85 A^7+119 A^6-51 A^5-19 A^4\) \(+95 A^3-133 A^2+58 A+I=\)TS EAMCET 2020 Medium - If \(x=\left(\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{8}\right)\), then \(\frac{\sin x+\cos x}{\tan x}=\)TS EAMCET 2020 Easy
- If \(f\) is a real valued function from \(A\) onto \(B\) defined by \(f(x)=\frac{1}{\sqrt{|x-|x||}}\) then \(A \cap B=\)TS EAMCET 2024 Easy
- If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3+4 x^2-9 x-36\) \(=0\) and \(\alpha < \beta < \gamma\) then \(\alpha+2 \beta+3 \gamma=\)TS EAMCET 2023 Easy
- The sum of all the roots of the equation \(\left|\begin{array}{ccc}x & -3 & 2 \\ -1 & -2 & (x-1) \\ 1 & (x-2) & 3\end{array}\right|=0\) isTS EAMCET 2025 Medium
- \(\left(\frac{1+i}{1-i}\right)^4+\left(\frac{1-i}{1+i}\right)^4\) is equal toTS EAMCET 2013 Easy
More PYQs from TS EAMCET
- A solid sphere and a thin uniform circular disc of same radius are rolling down an inclined plane without slipping. If the acceleration of the sphere is \(3 \mathrm{~ms}^{-2}\), then the acceleration of the disc isTS EAMCET 2025 Medium
- The locus of a point such that the sum of its distances from the points \((0,2)\) and \((0,-2)\) is 6 , isTS EAMCET 2011 Medium
- The chemicals and the reaction conditions required for the preparation of ethane areTS EAMCET 2005 Easy
- If \(\alpha, \beta, 2 \beta\) are the real roots of the equation \(x^3-9 x^2+k=0\) and \(k \in \mathbb{R}-\{0\}\), then \(14 \beta=\)TS EAMCET 2022 Medium
- The compound in which the number of \(d \pi\) - \(p \pi\) bonds are equal to those present in \(\mathrm{ClO}_4^{-}\)TS EAMCET 2008 Hard
- The line \(y=m x+c\) intercepts the circle \(x^2+y^2=r^2\) in two distinct points, ifTS EAMCET 2002 Medium