AP EAMCET · Maths · Quadratic Equation
Let \(\alpha, \beta\) be the roots of the equation \(x^2-|a| x-|b|=0\) such that \(|\alpha| < |\beta|\). If \(|a| < \beta-1\), then the positive root of \(\log _{\mid \text {여 }}\left(\frac{x^2}{\beta^2}\right)-1=0\), is
- A \( < |\alpha|\)
- B \( < \alpha\)
- C \( < \beta\)
- D \( > \beta\)
Answer & Solution
Correct Answer
(D) \( > \beta\)
Step-by-step Solution
Detailed explanation
Given, \(\log _{|\alpha|}\left(\frac{x^2}{\beta^2}\right)=1\) \(\Rightarrow \quad \frac{x^2}{\beta^2}=|\alpha| \Rightarrow x^2=\beta^2|\alpha|\) and \(\alpha, \beta\) are roots of equation \(x^2-|a| x-|b|=0\)...(i) so,…
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
- The solution of the differential equation \(x \frac{d y}{d x}=y-x \tan \left(\frac{y}{x}\right)\) is (Here, \(k\) is an arbitrary constant)AP EAMCET 2019 Medium
- The area (in square unit) of the triangle formed by \(x+y+1=0\) and the pair of straight lines \(x^2-3 x y+2 y^2=0\) isAP EAMCET 2009 Medium
- The area (in sq. units) of the region lying in the first quadrant and enclosed by the -axis, the straight line and the circle isAP EAMCET 2018 Easy
- The pair of straight lines represented by the equation \(3 d x^2-5 x y+\left(d^2-2\right) y^2=0\). If the lines are perpendicular to each other, for how many values of \(d\) this condition will be satisfied?AP EAMCET 2020 Easy
- \[
\lim _{x \rightarrow 9} \frac{(2.5)^{81-x^2}-(0.4)^{x+9}}{x+9}=
\]AP EAMCET 2023 Easy - If the volume of a sphere increases at the rate of \(2 \pi \mathrm{cm}^3 / \mathrm{s}\), then the rate of increase of its radius (in \(\mathrm{cm} / \mathrm{s}\) ), when the volume is \(288 \pi \mathrm{cm}^3\), isAP EAMCET 2012 Easy
More PYQs from AP EAMCET
- \(\int \frac{1}{x^2\left(\sqrt{1+x^2}\right)} d x=\)AP EAMCET 2024 Easy
- \(\lim _{n \rightarrow \infty}\left(\frac{1}{1^2+n^2}+\frac{2}{2^2+n^2}+\frac{3}{3^2+n^2}+\ldots+\frac{n}{n^2+n^2}\right)=\)AP EAMCET 2025 Medium
- A block of mass \(2 \mathrm{~kg}\) is initially at rest on a horizontal frictionless surface. A horizontal force \(\overrightarrow{\mathbf{F}}=\left(9-x^2\right) \hat{\mathbf{i}}\) newtons acts on it, when the block is at \(x=0\). The maximum kinetic energy of the block between \(x=0\) and \(x=3 \mathrm{~m}\) in joule isAP EAMCET 2004 Medium
- The Poisson's ratio of a material is 0.4 . If a force is applied to a wire of this material, there is a decrease of cross-sectional area by \(2 \%\). The percentage increase in its length isAP EAMCET 2002 Medium
- Let the points \(\mathrm{P}_1\left(\frac{\pi}{4}\right), \mathrm{P}_2\left(\frac{3 \pi}{4}\right), \mathrm{P}_3\left(\frac{5 \pi}{4}\right)\) and \(\mathrm{P}_4\left(\frac{7 \pi}{4}\right)\) given in parametric form, lie on the hyperbola \(\frac{x^2}{9}-\frac{y^2}{16}=1\). Then these four points in that order formAP EAMCET 2023 Easy
- A carrier wave of peak voltage \(15 \mathrm{~V}\) is used to transmit a message signal. If the modulation index is \(60 \%\), then the peak voltage of the modulating signal isAP EAMCET 2023 Easy