AP EAMCET · Maths · Quadratic Equation
If \(\alpha\) and \(\beta(\alpha>\beta)\) are the multiple roots of the equation \(4 x^4+4 x^3-23 x^2-12 x\) \(+36=0\), then \(2 \alpha-\beta=\)
- A \(-1\)
- B \(3\)
- C \(5\)
- D \(-7\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
\(P'(x) = 16x^3+12x^2-46x-12\). Solving \(P'(x)=0\) yields roots \(x=-2, x=\frac{3}{2}, x=-\frac{1}{4}\). Substituting into \(P(x)\): \(P(-2)=0\) and \(P(\frac{3}{2})=0\). Thus, \(\alpha=\frac{3}{2}\) and \(\beta=-2\) (since \(\alpha>\beta\)).…
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
- A true statement among the following identities isAP EAMCET 2022 Medium
- It \(\mathbf{a}, \mathbf{b}\) and \(\mathbf{c}\) are non-coplanar vectors and the four points with position vectors \(2 \mathbf{a}+3 \mathbf{b}-\mathbf{c}\), \(\mathbf{a}-2 \mathbf{b}+3 \mathbf{c}, 3 \mathbf{a}+4 \mathbf{b}+2 \mathbf{c}\) and \(k \mathbf{a}-6 \mathbf{b}+6 \mathbf{c}\) are coplanar, then \(k=\)AP EAMCET 2018 Easy
- If \(x=a\) is a root of multiplicity two of a polynomial equation \(f(x)=0\), thenAP EAMCET 2016 Medium
- If \(x\)-coordinate of a point \(P\) on the line joining the points \(Q(2,2,1)\) and \(R(5,1,-2)\) is 4 , then the \(z\)-coordinate of \(P\) isAP EAMCET 2012 Easy
- \(\vec{a}\) and \(\vec{b}\) are two vectors such that \(\vec{a}\) is not parallel to \(\vec{b}\). If \(\overrightarrow{\mathrm{p}}=(\mathrm{x}+2 \mathrm{y}+3) \overrightarrow{\mathrm{a}}+(5 \mathrm{x}-\mathrm{y}+2) \overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{q}}=(2 \mathrm{x}+3 \mathrm{y}+5)\) \(\vec{a}+(x-5 y-2) \vec{b}\) are two vectors such that \(\vec{p}=2 \vec{q}\), then \(\mathrm{x}-2 \mathrm{y}=\)AP EAMCET 2023 Easy
- The equations of tangents to the circle \(x^2+y^2=10\) from the point \((4,-2)\) areAP EAMCET 2020 Easy
More PYQs from AP EAMCET
- If \(\bar{a}=\bar{i}+4 \bar{j}-4 \bar{k}, \bar{b}=-2 \bar{i}+5 \bar{j}-2 \bar{k}\) and \(\bar{c}=3 \bar{i}-2 \bar{j}-4 \bar{k}\) are three vectors such that \((\bar{b} \times \bar{c}) \times \bar{a}=x \bar{i}+y \bar{j}+z \bar{k}\) then \(x+y-z=\)AP EAMCET 2025 Medium
- A monochromatic light of wavelength \(6000 Å\) coming from a star is detected in a 100 inch telescope. The limit of resolution of the telescope is approximatelyAP EAMCET 2022 Easy
- If a line makes angles \(90^{\circ}, 135^{\circ}\) and \(45^{\circ}\) with the positive directions of \(X, Y, Z\)-axes respectively. Then, its direction cosines areAP EAMCET 2020 Easy
- If thenAP EAMCET 2021 Medium
- Two statements are given below.
Statement-I: The ratio of the molar volume of a gas to that of an ideal gas at constant temperature and pressure is called the compressibility factor.
Statement-II: The RMS velocity of a gas is directly proportional to square root of \(\mathrm{T}(\mathrm{K})\)
The correct answer isAP EAMCET 2024 Medium - If the tangents of the parabola \(y^2=8 x\) passing through the point \(P(1,3)\) touches the parabola at \(A\) and \(B\), then the area (in sq. units) of \(\triangle A B C\) isAP EAMCET 2025 Medium