AP EAMCET · Maths · Quadratic Equation
If the roots of the equation \(x^3-13 x^2+\mathrm{K} x-27=0\) are in geometric progression then \(\mathrm{K}=\)
- A \(-30\)
- B \(30\)
- C \(39\)
- D \(-39\)
Answer & Solution
Correct Answer
(C) \(39\)
Step-by-step Solution
Detailed explanation
Given the equation, \(x^3-13 x^2+K x-27=0\) Let roots are \(\frac{a}{r}, a, a r\) Now, \(\frac{a}{r} \cdot a \cdot a r=\frac{-(-27)}{1} \Rightarrow a^3=27 \Rightarrow a=3\) and, \(\frac{3}{r}+3+3 r=\frac{-(-13)}{1} \Rightarrow \frac{3}{r}+3 r=10 \Rightarrow r=3, \frac{1}{3}\)…
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 \(f(x)=\left\{\begin{array}{cc}\frac{x-|x|}{x}, & \text { when } x < 0 \\ b\left(\frac{5 x^2+a,}{x^2-3 x+2}\right), & \text { when } 0 \leq x \leq 1 \\ -14, & \text { when } x \geq 3\end{array}\right.\) is a continuous function on \(R\), then \((a, b)=\)AP EAMCET 2019 Medium
- \(\int\left(\sum_{r=0}^{\infty} \frac{x^r 2^r}{r!}\right) d x=\)AP EAMCET 2025 Medium
- In a \(\triangle A B C, \cos \left(\frac{B+2 C+3 A}{2}\right)+\cos \left(\frac{A-B}{2}\right)\) is equal toAP EAMCET 2004 Medium
- If \(\Delta_k=\left|\begin{array}{ccc}1 & 0 & 0 \\ 0 & k & k-1 \\ 0 & k-1 & k\end{array}\right|\), then \(\Delta_1+\Delta_2+\ldots+\Delta_{20}\) is equal toAP EAMCET 2021 Easy
- The number of integer solutions of the equation isAP EAMCET 2022 Hard
- In a triangle ABC, if \(\mathrm{A}, \mathrm{B}\) and C are in arithmetic progression, \(rr_3=r_1 r_2\) and \(c=10\), then \(a^2+b^2+c^2=\)AP EAMCET 2025 Medium
More PYQs from AP EAMCET
- If the slope of one of the lines in the pair of lines \(8 x^2+a x y+y^2=0\) is thrice the slope of the second line, then \(a=\)AP EAMCET 2024 Easy
- The angle of projection of a projectile whose path is shown in the given figure is
AP EAMCET 2025 Medium - If \(\theta=\frac{\pi}{6}\) and \(x=\log \left[\cot \left(\frac{\pi}{4}+\theta\right)\right]\), then \(\sin h(x)=\)AP EAMCET 2019 Medium
- The time required for completion of of a first order reaction is minutes. The half life of it (in minutes) isAP EAMCET 2012 Easy
- All the letters of the word ANIMAL are permuted in all possible ways and the permutations thus formed are arranged in dictionary order. If the rank of the word ANIMAL is \(x\), then the permutation with rank \(x\), among the permutations obtained by permuting the letters of the word PERSON and arranging the permutations thus formed in dictionary order isAP EAMCET 2019 Medium
- Find the equation of the circle which passes through origin and cuts off the intercepts and over the and axes respectively.AP EAMCET 2021 Easy