TS EAMCET · Maths · Quadratic Equation
Let \(f(x)=x^2+a x+b\), where \(a, b \in R\). If \(f(x)=0\) has all its roots imaginary, then the roots of \(f(x)+f^{\prime}(x)+f^{\prime \prime}(x)=0\) are
- A real and distinct
- B imaginary
- C equal
- D rational and equal
Answer & Solution
Correct Answer
(B) imaginary
Step-by-step Solution
Detailed explanation
Given, \(f(x)=x^2+a x+b\) has imaginary roots. \(\therefore\) Discriminant, \(D < 0 \Rightarrow a^2-4 b < 0\) Now, \(\begin{aligned} f^{\prime}(x) & =2 x+a \\ f^{\prime \prime}(x) & =2 \end{aligned}\)…
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 a line L passing through a point \(\mathrm{A}(2,3)\) intersects another line \(4 x-3 y-19=0\) at the point \(B\) such that \(A B=4\), then the angle made by the line \(L\) with positive \(X\)-axis in anti-clockwise direction isTS EAMCET 2025 Medium
- The equation having the multiple root of the equation \(x^4+4 x^3-16 x-16=0\) as its root isTS EAMCET 2025 Medium
- If \({ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3\), then the minimum value of \(n\) isTS EAMCET 2011 Easy
- If and are the roots of the quadratic equation thenTS EAMCET 2019 Easy
- The shortest distance between the lines \(\mathbf{r}=3 \mathbf{i}+5 \mathbf{j}+7 \mathbf{k}+\lambda(\mathbf{i}+2 \mathbf{j}+\mathbf{k}) \quad\) and \(\mathbf{r}=-\mathbf{i}-\mathbf{j}-\mathbf{k}+\mu(7 \mathbf{i}-6 \mathbf{j}+\mathbf{k})\) isTS EAMCET 2013 Medium
- \(A(1,2,3), B(2,3,1)\) and \(C(3,1,2)\) are three points. If the point \(\mathrm{P}\) divides \(\mathrm{AB}\) in the ratio \(1: 2\) and the point \(\mathrm{Q}\) divides \(\mathrm{BC}\) in the ratio \(-2: 3\), then the distance between \(P\) and \(Q\) isTS EAMCET 2023 Easy
More PYQs from TS EAMCET
- A litre of seawater (which weighs ) contains of dissolved oxygen. The concentration of dissolved oxygen in is:TS EAMCET 2018 Medium
- For the reaction, \(0.5 \mathrm{C}(s)+0.5 \mathrm{CO}_2(g) \rightleftharpoons \mathrm{CO}(g)\) the equilibrium pressure is \(12 \mathrm{~atm}\). If, \(\mathrm{CO}_2\) conversion is \(50 \%\), the value of \(K_p\), in atm isTS EAMCET 2019 Medium
- Using mathematical induction, the numbers \(a_n\) 's are defined by, \(a_0=1, a_{n+1}=3 n^2+n+a_n,(n \geq 0) .\) Then, \(a_n\) is equal toTS EAMCET 2009 Easy
- If \(\frac{x+1}{x^4(x+2)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{x^4}+\frac{E}{x+2}\), then \(B+D+E\) is equal toTS EAMCET 2016 Easy
- If \(\mathrm{a}\) and \(\mathrm{b}\) are the arbitrary constants, then the differential equation corresponding to the family of curves given by \(y=x[a \cos (\log x)+b \sin (\log x)]\) isTS EAMCET 2023 Easy
- The driver of a bus moving with a velocity of 72 kmph observes a boy walking across the road at a distance of 50 m in front of the bus and decelerates the bus at \(5 \mathrm{~ms}^{-2}\) by applying brakes and is just able to avoid an accident. The reaction time of the driver isTS EAMCET 2025 Medium