AP EAMCET · Maths · Quadratic Equation
If \(x^2+p x+1\) is a factor of \(a x^3+b x+c\), then
- A \(a^2+c^2=a b+3\)
- B \(a^2-c^2=a b\)
- C \(a^2-c^2=-a b\)
- D \(a^2+c^2=a b\)
Answer & Solution
Correct Answer
(B) \(a^2-c^2=a b\)
Step-by-step Solution
Detailed explanation
\begin{array}{r}a x-a p \\ x ^ { 2 } + p x + 1 \longdiv { a x ^ { 3 } + b x + c } \\ \mathrm{ax}^3+\mathrm{apx}^2+a x \\ -\quad-\quad- \\ -\mathrm{apx}^2+(\mathrm{b}-\mathrm{a}) \mathrm{x}+\mathrm{c} \\ -\mathrm{apx}^2-\mathrm{ap}^2 \mathrm{x}-\mathrm{ap} \\ +\quad+\quad+ \\…
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 length of the tangent drawn from the mid-point of the line joining the origin and the point \((4,-4)\), to the circle \(2 x^2+2 y^2-y=0\) is unitsAP EAMCET 2020 Medium
- When the axes are rotated through an angle \(\theta\) about origin in anticlockwise direction and then translated to the new origin \((2,-2)\), if the transformed equation of the equation of \(\mathrm{x}^2+\mathrm{y}^2=4\) is \(\mathrm{X}^2+\mathrm{Y}^2+\mathrm{aX}+\mathrm{bY}+\mathrm{c}=0\) then \(\mathrm{a}+\mathrm{b}+\mathrm{c}=\)AP EAMCET 2025 Medium
- The range of the real valued function
\(f(x)=\frac{15}{3 \sin x+4 \cos x+10}\) isAP EAMCET 2024 Easy - The vertices of the hyperbola \(7 x^2-49 y^2=343\) having eccentricity ' \(4 / 3^{\prime}\) isAP EAMCET 2020 Easy
- If \(Z\) is a complex number such that \(|Z| \leq 3\) and \(\frac{-\pi}{2} \leq a m p Z \leq \frac{\pi}{2}\), then the area of the region formed by locus of \(Z\) isAP EAMCET 2024 Easy
- The value of \(k\), if \((1,2),(k,-1)\) are conjugate points with respect to the ellipse \(2 x^2+3 y^2=6\) isAP EAMCET 2007 Hard
More PYQs from AP EAMCET
- The number of hydrogen molecules possible from its isotopes isAP EAMCET 2022 Easy
- If thenAP EAMCET 2021 Medium
- The values of \(\lambda\) and \(\mu\) for which the system of equations \(x+y+z=6, x+2 y+3 z=10, x+2 y+\lambda z=\mu\) has infinitely many solutions areAP EAMCET 2017 Medium
- If \(\mathrm{X}\) is a random variable with the following probability distribution
\(\begin{array}{|l|c|c|c|}
\hline \mathrm{X}=x & -3 & 6 & 9 \\
\hline \mathrm{P}(\mathrm{X}=x) & \frac{1}{6} & \frac{1}{2} & \frac{1}{3} \\
\hline
\end{array}\)
then the variance of \(\mathrm{X}\) isAP EAMCET 2017 Easy - Circles are drawn through the point \((2,0)\) to cut intercepts of length 5 units on the X -axis. If their centre lie in the first quadrant, then their equation isAP EAMCET 2025 Medium
- If -coordinate of a point on the line joining the points and is , then the -coordinate ofAP EAMCET 2022 Easy