AP EAMCET · Maths · Quadratic Equation
If the roots of the equation \(x^3+3 p x^2+3 q x-8=0\) are in an arithmetic progression then \(2 p^3-3 p q=\)
- A 8
- B -8
- C 4
- D -4
Answer & Solution
Correct Answer
(A) 8
Step-by-step Solution
Detailed explanation
\((a-d)+a+(a+d) = -3p \implies 3a = -3p \implies a = -p\) \((a-d)a(a+d) = -(-8) \implies a(a^2-d^2)=8\) \(-p((-p)^2-d^2)=8 \implies -p(p^2-d^2)=8 \implies -p^3+pd^2=8 \implies pd^2=p^3+8\) \((a-d)a+a(a+d)+(a-d)(a+d)=3q \implies 3a^2-d^2=3q\)…
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 the circle \(x^2+y^2+2 \alpha x+c=0\) lies completely inside the circle \(x^2+y^2+2 \beta x+c=0\), then which of the following holds?AP EAMCET 2022 Easy
- The pair of straight lines represented by the equation \(3 d x^2-5 x y+\left(d^2-2\right) y^2=0\). If the lines are perpendicular to each other, for how many values of \(d\) this condition will be satisfied?AP EAMCET 2020 Easy
- If a square matrix \(A\) is such that \(\left(A^T-\frac{1}{2} I\right)\left(A-\frac{1}{2} I\right)\) \(=\left(A^T+\frac{1}{2} I\right)\left(A+\frac{1}{2} I\right)=I\), where \(I\) is a unit matrix, then \(A\) isAP EAMCET 2021 Easy
- If \(\int e^x(1+x) \cdot \sec ^2\left(x e^x\right) d x\) \(=f(x)+\) constant, then \(f(x)\) is equal toAP EAMCET 2008 Medium
- For any integer \(n \geq 1\), the remainder when the expression \(n^5-5 n^3+4 n+139\) is divided by 120 isAP EAMCET 2017 Medium
- Equation of the locus of the centroid of the triangle whose vertices are \((a \cos k, a \sin k),(b \sin k,-b \cos k)\) and \((1,0)\), where \(k\) is a parameter, isAP EAMCET 2016 Easy
More PYQs from AP EAMCET
- The hybridisation of metals involved in the following complexes, respectively are \(\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-},\left[\mathrm{CoF}_6\right]^{3-}\)AP EAMCET 2022 Easy
- The minimum distance of a point on the curve \(y=x^2-4\) from the origin isAP EAMCET 2022 Easy
- If and , then impliesAP EAMCET 2021 Medium
- The mole fraction of a solute in one molal ethanolic solution would beAP EAMCET 2021 Easy
- A glass vessel of volume is completely filled with a liquid and its temperature is raised by . What volume of the liquid will flow over, if the coefficient of linear expansion of glass is and coefficient of volume expansion of the liquid isAP EAMCET 2021 Medium
- A metallic wire loop of side \((l) 0.1 \mathrm{~m}\) and resistance of \(1 \Omega\) is moved with a constant velocity in a uniform magnetic field of \(2 \mathrm{Wm}^{-2}\) as shown in the figure. The magnetic field is perpendicular to the plane of the loop. The loop is connected to a network of resistors. The velocity of loop so as to have a steady current of 1 mA in loop is
AP EAMCET 2024 Easy