AP EAMCET · Maths · Quadratic Equation
If \(\alpha+\beta=-2\) and \(\alpha^3+\beta^3=-56\), then the quadratic equation whose roots are \(\alpha\) and \(\beta\) is
- A \(x^2+2 x-16=0\)
- B \(x^2+2 x+15=0\)
- C \(x^2+2 x-12=0\)
- D \(x^2+2 x-8=0\)
Answer & Solution
Correct Answer
(D) \(x^2+2 x-8=0\)
Step-by-step Solution
Detailed explanation
Given that, \(\alpha+\beta=-2\) and \(\alpha^3+\beta^3=-56\) \[ \begin{array}{rlrl} \Rightarrow & & (\alpha+\beta)\left(\alpha^2+\beta^2-\alpha \beta\right) & =-56 \\ \Rightarrow & \alpha^2+\beta^2-\alpha \beta & =28 \end{array} \]…
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 \(\int \frac{1}{\left((x+4)^3(x+1)^5\right)^{1 / 4}} d x=A \cdot\left(\frac{x+4}{x+1}\right)^n+c\), thenAP EAMCET 2025 Medium
- If \(a, b\) and \(c\) are the roots of \(x^3+4 x+1=0\), then \(\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}=\)AP EAMCET 2018 Medium
- If \(y=\sin \left(m \sin ^{-1} x\right)\), then \(\left(1-x^2\right) y_2-x y_1\) is equal to \(\left(\right.\) Here, \(y_n\) denotes \(\left.\frac{d^n y}{d x^n}\right)\)AP EAMCET 2010 Easy
- If one root of the cubic equation \(x^3+36=7 x^2\) is double of another, then the number of negative roots areAP EAMCET 2022 Medium
- The locus of the point of intersection of the normals to the parabola \(x^2=8 y\), which are at right angles to each other, isAP EAMCET 2017 Medium
- The area (in sq units) of the equilateral triangle formed by the tangent at \((\sqrt{3}, 0)\) to the hyperbola \(x^2-3 y^2=3\) with the pair of asymptotes of the hyperbola isAP EAMCET 2012 Medium
More PYQs from AP EAMCET
- The solution set contained in \(\mathbb{R}^{+}\)of the inequation \(3^x+3^{1-x}-4 < 0\) isAP EAMCET 2017 Medium
- In \(\triangle A B C\), if \(\mathrm{A}\) is \((1,2), \mathrm{B}\) and \(\mathrm{C}\) lie on \(\mathrm{y}=\mathrm{x}+\alpha\) (where \(\alpha\) is variable), then the locus of the orthocenter of the triangle isAP EAMCET 2022 Medium
- The equation of normal at \((1,1)\) to the circle \(x^2+y^2-x-3 y-4=0\) isAP EAMCET 2020 Medium
- Which of the following species do not exist?AP EAMCET 2021 Easy
- Out of thirty points in a plane, eight of them are collinear. The number of straight lines that can be formed by joining these points, isAP EAMCET 2014 Hard
- Among the following, van der Waals' constant \(a\) would be maximum forAP EAMCET 2021 Easy