TS EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta\) are the roots of \(a x^2+b x+c=0\) then \(\left(\frac{\alpha}{a \beta+b}\right)^3-\left(\frac{\beta}{a \alpha+b}\right)^3=\)
- A 0
- B 1
- C \((a+b)^2\)
- D \((a-b)^2\)
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
Given, \(\alpha, \beta\) are roots of \(a x^2+b x+c=0\) \(\Rightarrow a \alpha^2+b \alpha+c=0\) and \(a \beta^2+b \beta+c=0\) \(\alpha(a \alpha+b)=-c\) and \(\beta(a \beta+b)=-c\) \(a \alpha+b=-\frac{c}{\alpha} \Rightarrow a \beta+b=-\frac{c}{\beta}\) Now…
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 a line in the space makes angle \(\alpha, \beta\) and \(\gamma\) with the coordinate axes, then \(\begin{aligned} \cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma+\sin ^2 \alpha & +\sin ^2 \beta \ & +\sin ^2 \gamma \text { equals } \end{aligned}\)TS EAMCET 2009 Medium
- If a line is common to the planes and then the direction cosines of the line areTS EAMCET 2022 Easy
- If \(m x-y+c=0\) is a normal at a point \(P\) on the parabola \(y^2=16 x\) and the focal distance of \(P\) is 40 units, then \(|c|=\)TS EAMCET 2020 Medium
- \(\int \frac{d x}{4+3 \cot x}=\)TS EAMCET 2024 Medium
- If \(|\bar{a}|=4,|\bar{b}|=5,|\bar{a}-\bar{b}|=3\) and \(\theta\) is the angle between the vectors \(\overline{\mathrm{a}}\) and \(\overline{\mathrm{b}}\), then \(\cot ^2 \theta=\)TS EAMCET 2023 Easy
- A plane \(\pi\) makes intercepts 3 and 4 respectively on \(Z\)-axis and \(X\)-axis. If \(\pi\) is parallel to \(Y\)-axis, then its equation is :TS EAMCET 2003 Medium
More PYQs from TS EAMCET
- If the sum of two particular roots of the equation \(x^4-4 x^3\) \(-7 x^2+22 x+24=0\) is equal to the sum of the remaining two roots, then the sum of the cubes of all the roots of this equation isTS EAMCET 2023 Medium
- By using the non-zero digits, the number of 5 digit numbers that can be formed so that each number has largest digit in its middle place and the digits in the number are different isTS EAMCET 2021 Easy
- \(2 \hat{i}-3 \hat{j}+\hat{k}\) and \(\hat{i}+2 \hat{j}-3 \hat{k}\) are the position vectors of two points \(A\) and \(B\) respectively and \(C\) divides \(A B\) in the ratio \(3: 2\). If \(3 \hat{i}-\hat{j}+2 \hat{k}\) is the position vector of a point \(D\), then the unit vector in the direction of \(\overrightarrow{C D}\) isTS EAMCET 2024 Medium
- The molality (in mol \(\mathrm{kg}^{-1}\) ) of 1 mole of solute in \(50 \mathrm{~g}\) of solvent isTS EAMCET 2019 Easy
- If \(f(x)=\tan ^{-1}\left(\frac{1}{\sin ^2 x+\sin x+1}\right)\) \(+\tan ^{-1}\left(\frac{1}{\sin ^2 x+3 \sin x+3}\right)+\tan ^{-1}\) \(\left(\frac{1}{\sin ^2 x+5 \sin x+7}\right)+\ldots+\) upto 10 terms
then \(f^{\prime}(0)=\)TS EAMCET 2020 Hard - If \(f: \mathbf{R} \rightarrow \mathbf{R}\) be defined by \(f(x)=x+2|x+1|+2|x-1|\), then the element in the co-domain, which has unique pre image in the domain isTS EAMCET 2020 Easy