TS EAMCET · Maths · Quadratic Equation
If \(\alpha\) and \(\beta\) are the roots of the equation \(a x^2+b x+c=0\) and the equation having roots \(\frac{1-\alpha}{\alpha}\) and \(\frac{1-\beta}{\beta}\) is \(p x^2+q x+r=0\), then \(r=\)
- A \(a+2 b\)
- B \(a b+b c+c a\)
- C \(a+b+c\)
- D \(a b c\)
Answer & Solution
Correct Answer
(C) \(a+b+c\)
Step-by-step Solution
Detailed explanation
We have, \(\alpha, \beta\) are the roots of the equations \(a x^2+b x+c=0\) \[ \therefore \quad \alpha+\beta=-\frac{b}{a}, \alpha \beta=\frac{c}{a} \] Equations whose roots are \(\frac{1-\alpha}{\alpha}\) and \(\frac{1-\beta}{\beta}\) are…
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
- thenTS EAMCET 2021 Medium
- If the conjugate of \((x+i y)(1-2 i)\) is \((1+i)\), thenTS EAMCET 2017 Easy
- If \(\alpha\) represent the square of the distance between the origin and the point of intersection of the lines \(x^2-y^2-x+3 y-2=0\) and \(\beta\) represent the product of the perpendicular distances from the origin on the pair of lines, then \(\alpha \beta=\)TS EAMCET 2020 Medium
- Let \([x]\) denote the greatest integer not more than \(x\). If \(A\) and \(B\) are the domains of the functions \(f(x)=\frac{x-[x]}{\sqrt{|x|-x}}\) and \(g(x)=\frac{x-[x]}{\sqrt{|x|+x}}\) respectively, thenTS EAMCET 2020 Easy
- TS EAMCET 2021 Easy
- If \(\mathbf{a}, \mathbf{b}, \mathbf{c}, \mathrm{d}\) are 4 vectors such that \(\mathbf{a} \cdot \mathbf{b}=0\), \(|\mathbf{a} \times \mathbf{c}|=|\mathbf{a}\|\mathbf{c}|,| \mathbf{a} \times \mathbf{d}|=| \mathbf{a}\| \mathbf{d}|\), then \([\mathbf{b c d}]=\)TS EAMCET 2018 Medium
More PYQs from TS EAMCET
- A vessel contains hydrogen and nitrogen gases in the ratio \(2: 3\) by mass. If the temperature of the mixture of the gases is \(30^{\circ} \mathrm{C}\), then the ratio of the average kinetic energies per molecule of hydrogen and nitrogen gases is (Molecular mass of hydrogen \(=2\) and molecular mass of nitrogen \(=28\) )TS EAMCET 2024 Easy
- The angle between the lines \(\hat{\mathbf{r}}=(2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}})+\lambda(\hat{\mathbf{i}}+4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \quad\) and \(\hat{\mathbf{r}}=(\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}})+\mu(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})\) isTS EAMCET 2014 Medium
- A hot body placed in air cools down to a lower temperature. The rate of decrease of temperature is proportional to the temperature difference from the surrounding. The body loses \(60 \%\) and \(80 \%\) of maximum heat it can loose in time \(t_1\) and \(t_2\) respectively. The ratio \(t_2 / t_1\) will beTS EAMCET 2019 Easy
- The hybridizations of the central atom in the molecules \(\mathrm{BF}_3, \mathrm{BeF}_2, \mathrm{BrF}_3\) are respectivelyTS EAMCET 2023 Medium
- The boiling point of hydrogen halides varies in the orderTS EAMCET 2021 Medium
- The speed of the water in a river is near the surface. If the coefficient of viscosity of water is and the depth of the river is , then the shearing stress between the horizontal layers of water isTS EAMCET 2020 Easy