AP EAMCET · Maths · Quadratic Equation
Let \(a, b, c, d \in R\). If the equations \(2 b x^2+3 c x-d=0\) and \(2 a x^2+3 b x+4 c=0\) have a common root and \(\frac{4 b c+a d}{k\left(b^2-a c\right)}=\frac{b d+4 c^2}{4 b c+a d^{\prime}}\), then \(k=\)
- A \(\frac{9}{2}\)
- B \(\frac{2}{9}\)
- C \(\frac{1}{9}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{9}{2}\)
Step-by-step Solution
Detailed explanation
It is given that the given quadratic equations \(2 b x^2+3 c x-d=0 \text { and }\) \(2 a x^2+3 b x+4 c=0\) have a common root, \(\left(6 b^2-6 a c\right)\left(12 c^2+3 b d\right)=(8 b c+2 a d)^2\) Then, \(6\left(b^2-a c\right) 3\left(4 c^2+b d\right)=4(4 b c+a d)^2\)…
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
- If the directrix of the parabola \(x^2+4 y-6 x+\lambda=0\) is \(y+1=0\), then which of the following is correct?AP EAMCET 2022 Easy
- The coefficient of \(x^5\) in \(\left(3+x+x^2\right)^6\) isAP EAMCET 2024 Easy
- The range of the real valued function \(f(x)=\sin ^{-1}\left(\frac{1+x^2}{2 x}\right)+\cos ^{-1}\left(\frac{2 x}{1+x^2}\right)\) isAP EAMCET 2024 Medium
- The angle between the lines represented by isAP EAMCET 2021 Medium
- If \(x^3+y^3=3 a x y\), then at \(\left(\frac{3 a}{2}, \frac{3 a}{2}\right)\) the value of \(3 a y^{\prime \prime}+40\) isAP EAMCET 2023 Easy
- Let a kind of bacteria grow following the function \(f(t)=t^4, t\) given in seconds. If the rate of growth of the bacteria after \(\mathrm{t}_0\) seconds is \(4000 /\) second, then \(\mathrm{t}_0=\)AP EAMCET 2017 Easy
More PYQs from AP EAMCET
- ft.\left|z-\frac{1+3 i}{2}\right|=\frac{\sqrt{10}}{2}\right\}\)
If \(P, Q\) and \(R\) are points, respectively representing the complex numbers \(z, z e^{\frac{i \pi}{3}}\) and \(z\left(1+e^{\frac{i \pi}{3}}\right)\) in argand plane, then the area of the triangle \(P Q R\), isAP EAMCET 2019 Easy - Which of the following is not correct?AP EAMCET 2007 Easy
- Which among the following is not a greenhouse gas?AP EAMCET 2021 Easy
- Statement (A) Two artificial satellites revolving in the same circular orbit have same period of revolution.
Statement (B) The orbital velocity is inversely proportional to the square root of radius of the orbit.
Statement (C) The escape velocity of the body is independent of the altitude of the point of projection.AP EAMCET 2022 Medium - What is the angle of banking of a railway track of radius of curvature \(250 \mathrm{~m}\), if the maximum velocity of the train is \(90 \mathrm{~km} / \mathrm{h}\) ? \(\left(g=10 \mathrm{~ms}^{-2}\right)\)AP EAMCET 2021 Medium
-
List - I (Polymers) List -II (Type) A. Buna - N - Rubber I Fibre B. Terylene II Thermosetting polymer C. Polystyrene III Elastomer D. Urea - Formaldehyderesin IV Thermoplastic polymer AP EAMCET 2024 Easy