JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If the value of real number \(a > 0\) for which \(x^2-5 a x\) \(+1=0\) and \(x^2-a x-5=0\) have a common real roots is \(\frac{3}{\sqrt{2 \beta}}\) then \(\beta\) is equal to
- A \(11\)
- B \(13\)
- C \(12\)
- D \(14\)
Answer & Solution
Correct Answer
(B) \(13\)
Step-by-step Solution
Detailed explanation
`Two equations have common root \(\therefore(4 a)(26 a)=(-6)^2=36\) \(\Rightarrow a^2=\frac{9}{26} \quad \therefore a=\frac{3}{\sqrt{26}} \Rightarrow \beta=13\)
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 sum of the first \(20\) terms of the series \(5+11+\) \(19+29+41+\ldots\) is \(..........\).JEE Mains 2023 Hard
- Let \(\left(\begin{array}{l}n \\ k\end{array}\right)\) denotes \({ }^{n} C_{k}\) and \(\left[\begin{array}{l} n \\ k \end{array}\right]=\left\{\begin{array}{cc}\left(\begin{array}{c} n \\ k \end{array}\right), & \text { if } 0 \leq k \leq n \\ 0, & \text { otherwise }\end{array}\right.\) If \(A_{k}=\sum_{i=0}^{9}\left(\begin{array}{l}9 \\ i\end{array}\right)\left[\begin{array}{c}12 \\ 12-k+i\end{array}\right]+\sum_{i=0}^{8}\left(\begin{array}{c}8 \\ i\end{array}\right)\left[\begin{array}{c}13 \\ 13-k+i\end{array}\right]\) and \(A_{4}-A_{3}=190 \mathrm{p}\), then \(p\) is equal to :JEE Mains 2021 Hard
- Let \(A\) be a symmetric matrix such that \(|A|=2\) and \(\left[\begin{array}{ll}2 & 1 \\ 3 & \frac{3}{2}\end{array}\right] A =\left[\begin{array}{ll}1 & 2 \\ \alpha & \beta\end{array}\right]\). If the sum of the diagonal elements of \(A\) is s, then \(\frac{\beta s}{\alpha^2}\) is equal to \(..........\).JEE Mains 2023 Hard
- Let \(\int x^3 \sin x \mathrm{~d} x=g(x)+C\), where \(C\) is the constant of integration. If \(8\left(g\left(\frac{\pi}{2}\right)+g^{\prime}\left(\frac{\pi}{2}\right)\right)=\alpha \pi^3+\beta \pi^2+\gamma, \alpha, \beta, \gamma \in Z\), then \(\alpha+\beta-\gamma\) equals :JEE Mains 2025 Medium
- The coefficient of \(x^{-5}\) in the binomial expansion of \({\left( {\frac{{x + 1}}{{{x^{\frac{2}{3}}} - {x^{\frac{1}{3}}} + 1}} - \frac{{x - 1}}{{x - {x^{\frac{1}{2}}}}}} \right)^{10}}\) where \(x \ne 0, 1\) , isJEE Mains 2017 Hard
- If the functions \(f ( x )=\frac{ x ^3}{3}+2 bx +\frac{a x^2}{2}\) and \(g(x)=\frac{x^3}{3}+a x+b x^2, a \neq 2 b\) have a common extreme point, then \(a+2 b+7\) is equal toJEE Mains 2023 Hard
More PYQs from JEE Mains
- Let \(A = \left\{ {\left( {x,y} \right):{y^2} \le 4x,y - 2x \ge - 4} \right\}\) .The area of the region \(A\) isJEE Mains 2014 Hard
- Let \(b _{1} b _{2} b _{3} b _{4}\) be a \(4\)-element permutation with \(b _{i} \in\) \(\{1,2,3, \ldots \ldots . .100\}\) for \(1 \leq i \leq 4\) and \(b_{i} \neq b_{j}\) for \(i \neq j\), such that either \(b _{1}, b _{2}, b _{3}\) are consecutive integers or \(b _{2}, b _{3}, b _{4}\) are consecutive integers.JEE Mains 2022 Hard
- If \(\sum_{r=1}^{13}\left\{\frac{1}{\sin \left(\frac{\pi}{4}+(r-1) \frac{\pi}{6}\right) \sin \left(\frac{\pi}{4}+\frac{r \pi}{6}\right)}\right\}=a \sqrt{3}+b, a, b \in \mathbf{Z}\), then \(a^2+b^2\) is equal to :JEE Mains 2025 Hard
- Let \(A=\left(\begin{array}{ccc}{[x+1]} & {[x+2]} & {[x+3]} \\ {[x]} & {[x+3]} & {[x+3]} \\ {[x]} & {[x+2]} & {[x+4]}\end{array}\right),\) where \([t]\) denotes the greatest integer less than or equal to \(\mathrm{t}\). If \(\operatorname{det}(\mathrm{A})=192\), then the set of values of \(\mathrm{x}\) is the intervalJEE Mains 2021 Hard
- Let \(y=y(x)\) be the solution of the differential equation \((x+y+2)^2 d x=d y, y(0)=-2\). Let the maximum and minimum values of the function \(y=y(x)\) in \(\left[0, \frac{\pi}{3}\right]\) be \(\alpha\) and \(\beta\), respectively. If \((3 \alpha+\pi)^2+\beta^2=\gamma+\delta \sqrt{3}, \gamma, \delta \in \mathbb{Z}\), then \(\gamma+\delta\) equals ....................JEE Mains 2024 Hard
- If \(P ( h , k )\) be point on the parabola \(x =4 y ^2\), which is nearest to the point \(Q(0,33)\), then the distance of \(P\) from the directrix of the parabola \(y ^2=4( x + y )\) is equal to :JEE Mains 2023 Hard