AP EAMCET · Maths · Quadratic Equation
If \((x-2)\) is a common factor of the expressions \(x^2+a x+b\) and \(x^2+c x+d\), then \(\frac{b-d}{c-a}\) is equal to
- A \(-2\)
- B \(-1\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
Since, \((x-2)\) is a common factor of the expressions \(x^2+a x+b\) and \(x^2+c x+d\) \(\Rightarrow \quad 4+2 a+b=0...(i)\) and \(4+2 c+d=0...(ii)\) \(\begin{array}{rlrl}\Rightarrow & 2 a+b =2 c+d \\ \Rightarrow & b-d =2(c-a) \\ \Rightarrow & \frac{b-d}{c-a} =2\end{array}\)
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 \(f(x)\)
\(\left|\begin{array}{ccc}1 & x & x+1 \\ 2 x & x(x-1) & x(x+1) \\ 3 x(x-1) & x(x-1)(x-2) & (x-1) x(x+1)\end{array}\right|\)
then \(f(2012)\) is equal toAP EAMCET 2012 Medium - If a real valued function
\(f(x)=\left\{\begin{array}{cl}\frac{2 x^2+(k+2) x+9}{3 x^2-7 x-6} & , \text { for } x \neq 3 \\ l & , \text { for } x=3\end{array}\right.\)
\(x=3\) and \(l\) is a finite value, then \(l-k=\)AP EAMCET 2024 Easy - The range of the data \(35,12,21,24,15,7,16\), \(12,30,32,13,17\) isAP EAMCET 2022 Easy
- \(\int_0^{\pi / 2} \operatorname{Sin}^8 x d x=\)AP EAMCET 2017 Easy
- If \(f: R \rightarrow R\) is an even function which is twice differentiable on \(R\) and \(f^{\prime \prime}(\pi)=1\), then \(f^{\prime \prime}(-\pi)\) is equal toAP EAMCET 2005 Medium
- Which of the following is false?
1. If \((a, b, c)\) are direction ratios of a line, then \(a^2+b^2+c^2 \neq 1\).
2. The direction cosines of a line can be its direction ratios but not vice-versa.
3. If \((l, m, n)\) is one set of direction cosines, then \((-l,-m,-n)\) is also a valid set.
4. If \(\left(l_1, m_1, n_1\right)\) and \(\left(l_2, m_2, n_2\right)\) are direction cosines of perpendicular lines, then \(l_1 l_2+m_1 m_2+n_1 n_2=1\).AP EAMCET 2020 Easy
More PYQs from AP EAMCET
- Which of the following is an example of a multi molecular colloid?AP EAMCET 2023 Easy
- A resistance \(R\) is connected to ' \(n\) ' identical cells. If the current in the resistance is same whether the cells are connected either in series or in parallel, then the internal resistance (r) of each cell isAP EAMCET 2017 Easy
- Observe the following molecules: \(\mathrm{C}_2, \mathrm{~N}_2, \mathrm{O}_2, \mathrm{~F}_2\) Which one of the following statements is correct for the above molecules?AP EAMCET 2019 Hard
- Choose the correct option regarding the following statements:
StatementNitrogen has lesser electron gain enthalpy than oxygen.
Statement Oxygen has lesser ionization enthalpy than nitrogen.AP EAMCET 2021 Easy - If \(A=\left[\begin{array}{lll}83 & 74 & 41 \\ 93 & 96 & 31 \\ 24 & 15 & 79\end{array}\right]\), then \(\operatorname{det}\left(A-A^{\mathrm{T}}\right)=\)AP EAMCET 2024 Easy
- In Young's double slit experiment, the two slits are illuminated by a light beam consisting of wavelengths \(4200 Å\) and \(5040 Å\). If the distance between the slits is \(2.4 \mathrm{~mm}\) and the distance between the slits and the screen is \(200 \mathrm{~cm}\), the minimum distance from the central bright fringe to the point where the bright fringes due to both the wavelengths coincide isAP EAMCET 2018 Hard