WBJEE · Maths · Basic of Mathematics
The equation \(x^{\left(\log _{3} x\right)^{2}-\frac{9}{2} \log _{3} x+5}=3 \sqrt{3}\) has
- A at least one real root
- B exactly one real root
- C exactly one irrational root
- D complex roots
Answer & Solution
Correct Answer
(C) exactly one irrational root
Step-by-step Solution
Detailed explanation
Hint \(: 2 t^{3}-9 t^{2}+10 t-3=0, t=\log _{3} x\) \(\Rightarrow(t-3)(t-1)\left(t-\frac{1}{2}\right)=0\) \(\Rightarrow x=3^{3}, 3^{1}, 3^{1 / 2}\)
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
- On the set \(R\) of real numbers, the relation \(\rho\) is defined by \(x \rho y,(x, y) \in R\)WBJEE 2018 Easy
- In the set of all \(3 \times 3\) real matrices a relation is defined as follows. A matrix \(A\) is related to a matrix \(B,\) if and only if there is a non-singular \(3 \times 3\) matrix \(P,\) such that \(B=P^{-1} A P .\) This relation isWBJEE 2013 Medium
- Let the coefficients of powers of \(x\) in the \(2 n d\), 3rd and 4 th terms in the expansion of \((1+x)^{n}\) where \(n\) is a positive integer, be in arithmetic progression. Then, the sum of the coefficients of odd powers of \(x\) in the expansion isWBJEE 2012 Medium
- Let \(A\) and \(B\) are orthogonal matrices and \(\operatorname{det} A+\operatorname{det} B=0\). ThenWBJEE 2023 Hard
- If \(x\) and \(y\) are digits such that \(17 !=3556xy428096000,\) then \(x+y\) equalsWBJEE 2015 Medium
- The value of \(\cos 15^{\circ}-\sin 15^{\circ}\) isWBJEE 2011 Medium
More PYQs from WBJEE
- Ozonolysis of an alkene produces only one dicarbonyl compound. The structure of the alkene isWBJEE 2016 Medium
- The total number of alkyl bromides (including stereoismers) formed in the reaction \(\mathrm{Me}_{3} \mathrm{C}-\mathrm{CH}=\mathrm{CH}_{2}+\mathrm{HBr} \rightarrow\) will beWBJEE 2020 Medium
- The atomic masses of helium and neon are \(4.0\) and \(20.0\) amu respectively. The value of the de Broglie wavelength of helium gas at \(-73^{\circ} \mathrm{C}\) is \(\mathrm{M}\) times the de Broglie wavelength of neon at \(727^{\circ} \mathrm{C}\). The value of \(\mathrm{M}\) isWBJEE 2021 Medium
- If \(\operatorname{adj} \mathrm{B}=\mathrm{A},|\mathrm{P}|=|\mathrm{Q}|=1\), then \(\operatorname{adj}\left(\mathrm{Q}^{-1} \mathrm{BP}^{-1}\right)=\)WBJEE 2025 Medium
- The roots of the quadratic equation \(x^2-2 \sqrt{3} x-22=0\) are :WBJEE 2010 Easy
- Find the maximum value of \(|z|\) when \(\left|z-\frac{3}{z}\right|=2,\) where \(z\) being a complex number.WBJEE 2015 Easy