TS EAMCET · Maths · Quadratic Equation
The roots of the equation \(x^4+x^3-4 x^2+x+1=0\) are diminished by \(h\) so that the transformed equation does not contain \(\mathrm{x}^2\) term. If the values of such \(\mathrm{h}\) are \(\alpha\) and \(\beta\), then \(12(\alpha-\beta)^2=\)
- A \(35\)
- B \(25\)
- C \(105\)
- D \(115\)
Answer & Solution
Correct Answer
(A) \(35\)
Step-by-step Solution
Detailed explanation
\(x^4+x^3-4 x^2+x+1=0\) \[ =(x-1)^2\left(x^2+3 x+1\right)=0 \] \(\therefore\) roots are \(1,1, \frac{-3 \pm \sqrt{5}}{2}\) Let \(\alpha=1, \beta=1, \gamma=\frac{-3+\sqrt{5}}{2}, \delta=\frac{-3-\sqrt{5}}{2}\) Coefficient of \(x^2=\Sigma \alpha \beta\)…
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
- If \(\frac{1}{2 \times 4}+\frac{1}{4 \times 6}+\frac{1}{6 \times 8}+\ldots(n\) terms \()=\frac{k n}{n \times 1}\), then \(k\) is equal toTS EAMCET 2012 Medium
- The period of \(\cos \left(x+8 x+27 x+\ldots+n^3 x\right)\) isTS EAMCET 2019 Easy
- If \(y=\frac{\log _e x}{x}\) and \(z=\log _e x\), then \(\frac{d^2 y}{d z^2}+\frac{d y}{d z}\) is equal toTS EAMCET 2011 Easy
- If thenTS EAMCET 2019 Medium
- If \(y=\frac{a x+b}{c x+d}\), than \(\frac{d x}{d y}=\)TS EAMCET 2022 Easy
- The transformed equation of \(x^2+6 x y+8 y^2=10\) when the axes are rotated through an angle \(\frac{\pi}{4}\) is :TS EAMCET 2006 Medium
More PYQs from TS EAMCET
- If the incentre and the circumcentre of the triangle formed by the lines , and are and respectively, thenTS EAMCET 2022 Medium
- The total number of overlapping \(p\)-orbitals present in cycloheptatrienyl cation isTS EAMCET 2021 Medium
- The position vector of a point \(P\) is \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\mathbf{a}=-\hat{\mathbf{i}}-2 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are two vectors which determine a plane \(\pi\). The equation of a line through \(P\) normal to \(\mathbf{b}\) and lying on the plane \(\pi\) isTS EAMCET 2020 Easy
- An electron beam travels with a velocity of \(1.6 \times 10^7 \mathrm{~ms}^{-1}\) perpendicularly to magnetic field of intensity \(0.1 \mathrm{~T}\). The radius of the path of the electron beam \(\left(m_e=9 \times 10^{-31} \mathrm{~kg}\right.\) )TS EAMCET 2007 Easy
- Which of the following are correct? (1) Electron density in \(X Y\) plane for \(d_{x^2-y^2}\) orbital is zero. (2) The energy of \(3 p\)-orbital is higher than the energy of \(2 p\)-orbital. (3) \(3 p_z\)-orbital has one angular node. (4) 4 -orbital has no radial node.TS EAMCET 2018 Medium
- A solid has hcp lattice. Atoms of \(Z\) (anions) form hcp lattice. Atoms of \(X\) (cations) occupy all the octahedral voids in the lattice. Atoms of \(Y\) (cations) occupy half of the tetrahedral voids. What is the molecular formula of the solid?TS EAMCET 2018 Medium