JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(\alpha, \beta\) be the roots of the equation \(x^2+2 \sqrt{2} x-1=0\). The quadratic equation, whose roots are \(\alpha^4+\beta^4\) and \(\frac{1}{10}\left(\alpha^6+\beta^6\right)\), is :
- A \(x^2-190 x+9466=0\)
- B \(x^2-195 x+9466=0\)
- C \(x^2-195 x+9506=0\)
- D \(x^2-180 x+9506=0\)
Answer & Solution
Correct Answer
(C) \(x^2-195 x+9506=0\)
Step-by-step Solution
Detailed explanation
\( x^2+2 \sqrt{2} x-1=0 \) \( \alpha+\beta=-2 \sqrt{2} \) \( \alpha \beta=-1 \) \( \alpha^4+\beta^4=\left(\alpha^2+\beta^2\right)^2-2 \alpha^2 \beta^2 \) \( =\left((\alpha+\beta)^2-2 \alpha \beta\right)^2-2(\alpha \beta)^2 \) \( =(8+2)^2-2(-1)^2 \) \( =100-2=98 \)…
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
- \(ABC\) is a triangular park with \(AB = AC = 100\) \(metres\). A vertical tower is situated at the mid-point of \(BC\). If the angles of elevation of the top of the tower at \(A\) and \(B\) are \({\cot ^{ - 1}}\left( {3\sqrt 2 } \right)\) and \(\cos e{c^{ - 1}}\left( {2\sqrt 2 } \right)\) respectively, then the height of the tower (in metres) isJEE Mains 2019 Hard
- The value of \(\lim\limits _{n \rightarrow \infty} 6 \tan \left\{\sum\limits_{r=1}^{n} \tan ^{-1}\left(\frac{1}{r^{2}+3 r+3}\right)\right\}\) is equal toJEE Mains 2022 Hard
- Let \(K\) be the set of all real values of \(x\) where the function \(f\left( x \right) = \sin \,\left| x \right| - \left| x \right| + 2\,\left( {x - \pi } \right)\,\cos \,\left| x \right|\) is not differentiable. Then the set \(K\) is equal toJEE Mains 2019 Hard
- Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If \(x\) denote the number of defective oranges, then the variance of \(x\) isJEE Mains 2025 Medium
- If \(n\) be odd or even, then the sum of \(n\) terms of the series \(1 - 2 + \) \(3 - \)\(4 + 5 - 6 + ......\) will beJEE Mains 2022 Easy
- The number of common tangents, to the circles \(x^2+y^2-18 x-15 y+131=0\) and \(x^2+y^2-6 x-6 y-7=0\), is :JEE Mains 2023 Medium
More PYQs from JEE Mains
- Let \(P\) be the plane, which contains the line of intersection of the planes, \(x + y + z - 6 = 0\) and \(2x + 3y + z + 5 = 0\) and it is perpendicular to the \(xy -\) plane. Then the distance of the point \((0, 0, 256)\) from \(P\) is equal toJEE Mains 2019 Hard
- If \(\smallint f\left( x \right)\;dx = \varphi \left( x \right)\), then \(\smallint {x^5}\;f\left( {{x^3}} \right)\;dx = \)JEE Mains 2013 Hard
- Let \(A = \left\{ {\left( {x,y} \right):{y^2} \le 4x,y - 2x \ge - 4} \right\}\) .The area of the region \(A\) isJEE Mains 2014 Hard
- If \(\mathrm{U}_{\mathrm{n}}=\left(1+\frac{1}{\mathrm{n}^{2}}\right)\left(1+\frac{2^{2}}{\mathrm{n}^{2}}\right)^{2} \ldots\left(1+\frac{\mathrm{n}^{2}}{\mathrm{n}^{2}}\right)^{\mathrm{n}}\), then \(\lim _{n \rightarrow \infty}\left(U_{n}\right)^{\frac{-4}{n^{2}}}\) is equal to :JEE Mains 2021 Hard
- If \(y=y(x)\) is the solution of the differential equation \(\frac{d y}{d x}+\frac{4 x}{\left(x^2-1\right)} y=\frac{x+2}{\left(x^2-1\right)^{\frac{5}{2}}},x > 1\) such that \(y(2)=\frac{2}{9} \log _e(2+\sqrt{3})\) and \(y(\sqrt{2})=\) \(\alpha \log _e(\sqrt{\alpha}+\beta)+\beta-\sqrt{\gamma}, \alpha, \beta, \gamma \in N\), then \(\alpha \beta \gamma\) is equal to \(........\).JEE Mains 2023 Hard
- Let \(u=\frac{2 z+i}{z-k i}, z=x+i y\) and \(k>0 .\) If the curve represented by \(\operatorname{Re}( u )+\operatorname{Im}( u )=1\) intersects the \(y\)-axis at the points \(P\) and \(Q\) where \(P Q=5,\) then the value of \(k\) isJEE Mains 2020 Hard