TS EAMCET · Maths · Quadratic Equation
If the expression \(7+6 x-3 x^2\) attains its extreme value \(\beta\) at \(x=\alpha\), then the sum of the squares of the roots of the equation \(x^2+\alpha x-\beta=0\) is
- A 21
- B -19
- C 19
- D -21
Answer & Solution
Correct Answer
(A) 21
Step-by-step Solution
Detailed explanation
Given expression is \(7+6 x-3 x^2=f(x)\)...(i) Extreme value of \(f(x)\) is \(\beta=\frac{-D}{4 a}\) which occurs at \(\alpha=\frac{-b}{2 a}\) \(a=-3, b=6, c=7\) (on comparing (i) with \(a x^2+b x+c\) ) \(\beta=\frac{-(36+84)}{(4 \times-3)}=10 ; \alpha=\frac{-6}{-6}=1\)…
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 \(\frac{x^2}{2 x^4+7 x^2+6}=\frac{A x+B}{x^2+a}+\frac{C x+D}{a x^2+3}\), then \(A+B+C-2 D\)TS EAMCET 2024 Medium
- If \(A\) is a non singular matrix, then \(\operatorname{Adj}\left(A^{-1}\right)=\)TS EAMCET 2024 Easy
- \(\int_0^{\frac{\pi}{4}} \frac{\cos ^2 x}{\cos ^2 x+4 \sin ^2 x} d x=\)TS EAMCET 2019 Easy
- Let \(f(x)\) be continuous on \([0,4]\), differentiable on \((0,4), f(0)=4\) and \(f(4)=-2\). If \(g(x)=\frac{f(x)}{x+2}\), then the value of \(g^{\prime}(c)\) for some Lagrange's constant \(c \in(0,4)\) isTS EAMCET 2018 Easy
- A pair of dice is thrown twice in succession. The probability of getting prime numbers on both the dice in first throw and composite numbers on both the dice in second throw isTS EAMCET 2022 Medium
- In a triangle and divide the sides and in the ratio respectively. If is the point of intersection of and then the ratio in which divides isTS EAMCET 2022 Medium
More PYQs from TS EAMCET
- A force acts on a \(30 \mathrm{~g}\) particle in such a way that the position of the particle as a function of time is given by \(x=\alpha t^2\), where \(x\) is in metre, \(t\) is in seconds and \(\alpha=1 \mathrm{~m} / \mathrm{s}^2\). The work done during the first \(4 \mathrm{~s}\) isTS EAMCET 2020 Easy
- If \(\quad f:[2, \infty) \rightarrow B \quad\) defined by \(f(x)=x^2-4 x+5\) is a bijection, then \(B\) is equal toTS EAMCET 2011 Easy
- \(X\) reacts with dilute nitric acid to form 'laughing gas'. What is \(X\) ?TS EAMCET 2016 Easy
- Let \(a, b, c, d \in \mathbf{R}\) be such that \(a d-b c \neq 0\) and \(e\) be a positive number other than 1 . If \(x^a y^b=e^m, x^c y^d=e^n, \Delta_1=\left|\begin{array}{ll}m & b \\ n & d\end{array}\right|, \Delta_2=\left|\begin{array}{ll}a & m \\ c & n\end{array}\right|\) and \(\Delta_3=\left|\begin{array}{ll}a & b \\ c & d\end{array}\right|\), then the values of \(x\) and \(y\) are respectively.TS EAMCET 2020 Hard
- A thin wire of length \(l\) having density \(\rho\) is bent into a circular loop with \(C\) as its centre, as shown in figure. The moment of inertia of the loop about the line \(A B\) is
TS EAMCET 2014 Medium - The relative order of electronegativity of , and isTS EAMCET 2022 Easy