AP EAMCET · Maths · Quadratic Equation
The difference between two roots of the equation \(x^3-13 x^2+15 x+189=0\) is 2 . Then the roots of the equation are :
- A \(-3,5,7\)
- B \(-3,-7,-9\)
- C \(3,-5,7\)
- D \(-3,-7,9\)
Answer & Solution
Correct Answer
(A) \(-3,5,7\)
Step-by-step Solution
Detailed explanation
Let roots of the equation \(x^3-13 x^2+15 x+189=0\) are \(\alpha, \alpha+2\) and \(\beta\) \(\alpha+\alpha+2+\beta=13\) \(\ldots\) (i) \(\alpha(\alpha+2)+(\alpha+2) \beta+\alpha \beta=15\) \(\ldots\) (ii) and \(\quad \alpha(\alpha+2) \beta=-189\) \(\ldots\) (iii) These three…
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
- A game consists of tossing a coin 3 times and noting its outcome. A boy wins the game if all tosses give the same outcome (i.e three heads or three tails) and loses the game otherwise. The probability that the boy loses the game isAP EAMCET 2023 Easy
- If \(\operatorname{det}(\mathrm{AB})=(\operatorname{det} \mathrm{A})(\operatorname{det} \mathrm{B})\) and \(\mathrm{A}\) is a non-singular matrix of \(\operatorname{order} 3 \times 3\), then \(\operatorname{det}(\operatorname{adj} A)=\)AP EAMCET 2023 Easy
- The mean and variance of the observations \(\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3, \ldots, \mathrm{x}_{15}\) are respectively 2 and 4. If the mean and variance of the observations \(y_1, y_2, \ldots, y_{10}\) are respectively 2 and 5, then the variance of the observations \(\mathrm{x}_1, \mathrm{x}_2, \ldots \mathrm{x}_{15}, \mathrm{y}_1, \mathrm{y}_2, \ldots, \mathrm{y}_{10}\) isAP EAMCET 2025 Medium
- If \(f(x)=\sqrt{2 x-1}+5 \cos ^{-1}\left(\frac{2 x-1}{3}\right)\) then the domain of the function \(f(x)\) isAP EAMCET 2018 Medium
- The eccentricity of an ellipse, with its centre as origin, is \(1 / 2\). If one of the directrices is \(x=4\), then the equation of the ellipse is given byAP EAMCET 2020 Easy
- The length of the common chord of the circles \(x^2+y^2+3 x+5 y+4=0\) and \(x^2+y^2+5 x+3 y+4=0\) isAP EAMCET 2017 Easy
More PYQs from AP EAMCET
- The line \(y=6 x+1\) touches the parabola \(y^2=24 x\). The coordinates of a point \(P\) on this line, from which the tangent to \(y^2=24 x\) is perpendicular to the line \(y=6 x+1\), isAP EAMCET 2018 Easy
- If the position vectors of the vertices \(A, B, C\) of a triangle are \(3 \bar{i}+4 \bar{j}-\bar{k}\), \(\overline{\mathrm{i}}+3 \overline{\mathrm{j}}+\overline{\mathrm{k}}, 5(\overline{\mathrm{i}}+\overline{\mathrm{j}}+\overline{\mathrm{k}})\) respectively, then the magnitude of the altitude drawn from \(A\) on to the side \(B C\) isAP EAMCET 2025 Medium
- The number of \(d\) electrons in Fe is equal to which of the following?
i. Total number of ' \(s\) ' electrons of Mg
ii. Total number of ' \(p\) ' electrons of Cl
iii. Total number of ' \(p\) ' electrons of Ne
The correct option isAP EAMCET 2024 Easy - Let \(x, y\) be real numbers such that \(x \neq y\) and \(x y \neq 1\). If \(a x+b \sec \left(\tan ^{-1} x\right)=c\) and \(a y+b \sec \left(\tan ^{-1} y\right)=c\), then \(\frac{x+y}{1-x y}=\)AP EAMCET 2018 Medium
- Match the following List-I with the List-II
\begin{array}{|c|c|c|}
\hline List - I & & List - II \\
\hline A)Gauss's law & I) & Surface charge density \\
\hlineB) Faraday's law & II) & Electric charge and energy conservation \\
\hline C)Ampere's law & III) & Change in magnetic flux \\
\hline D) Kirchhoff's law & IV) & Change in electric flux \\
\hline & V) & Total electric flux \\
\hline
\end{array}
The correct answerAP EAMCET 2018 Easy - Find the equation of pair of straight lines that bisect the angles between the lines represented by \(a x^2+2 h x y+b y^2=0\).AP EAMCET 2020 Medium