WBJEE · Maths · Quadratic Equation
If \(\alpha\) and \(\beta\) are the roots of \(x^{2}-p x+1=0\) and \(\gamma\) is a root of \(x^{2}+p x+1=0,\) then \((\alpha+\gamma)(\beta+\gamma)\) is
- A 0
- B 1
- C -1
- D \(p\)
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
Since, \(\alpha\) and \(\beta\) are the roots of \(x^{2}-p x+1=0\). \(\therefore\) \(\alpha+\beta=p\) and \(\alpha \beta=1\) Also, \(\gamma\) is the root of \(x^{2}+p x+1=0\) \(\therefore \quad \gamma^{2}+p{\gamma}+1=0 \Rightarrow \gamma^{2}=-p \gamma-1\) Now,…
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
- \(\mathrm{I}=\int \cos (\ln \mathrm{x}) \mathrm{dx}\). Then \(\mathrm{I}=\)WBJEE 2022 Easy
- If \(A\) and \(B\) square matrices of the same order and \(A B=3 I\), then \(A^{-1}\) is equal toWBJEE 2009 Easy
- The equation of the plane through the intersection of the planes \(x+y+z=1\) and \(2 x+3 y-z+4\) and parallel to the \(x\)-axis isWBJEE 2022 Easy
- If the following three linear equations have a non-trivial solution, then
\[
\begin{array}{l}
x+4 a y+a z=0 \\
x+3 b y+b z=0 \\
x+2 c y+c z=0
\end{array}
\]WBJEE 2018 Easy - The incentre of an equilateral triangle is (1,1) and the equation of ene side is \(3 x+4 y+3=0 .\) Then, the equation of the circumeircle of the triangle isWBJEE 2012 Medium
- The function \(f(x)=a \sin |x|+b e^{| x \mid} \quad\) is differentiable at \(x=0\) whenWBJEE 2014 Medium
More PYQs from WBJEE
- The tangent at point \((a \cos \theta, b \sin \theta), 0 < \theta < \frac{\pi}{2}\), to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) meets the \(x\)-axis at \(T\) and \(y\)-axis at \(T_1\). Then the value of \(\min _{0 < \theta < \frac{\pi}{2}}(O T)\left(O T_1\right)\) isWBJEE 2023 Medium
- \(\lim _{x \rightarrow 0} \frac{\sin \left(\pi \sin ^2 x\right)}{x^2}=\)WBJEE 2011 Easy
- A biased coin with probability \(p(0 \lt p \lt 1)\) of getting head is tossed until a head appears for the first time. If the probability that the number of tosses required is even is \(\frac{2}{5}\), then \(p=\)WBJEE 2024 Medium
- Consider a particle of mass 1 gm and charge 1.0 Coulomb is at rest. Now the particle is subjected to an electric field \(E(t)=E_0 \sin \omega t\) in the \(x\)-direction, where \(E_0=2\) Newton/Coulomb and \(\omega=1000 \mathrm{rad} / \mathrm{sec}\). The maximum speed attained by the particle isWBJEE 2025 Medium
- Which of the following species exhibits both LMCT and paramagnetism?WBJEE 2024 Medium
- The yield of a acetanilide in the reaction (100\% conversion) of 2 moles of aniline with 1 mole of acetic anhydride isWBJEE 2017 Easy