WBJEE · Maths · Quadratic Equation
If \(\alpha, \beta\) be the roots of \(x^2-a(x-1)+b=0\), then the value of \(\frac{1}{\alpha^2-a \alpha}+\frac{1}{\beta^2-a \beta}+\frac{2}{a+b}\)
- A \(\frac{4}{a+b}\)
- B \(\frac{1}{a+b}\)
- C 0
- D -1
Answer & Solution
Correct Answer
(C) 0
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { Hints }: x^2-a x=a+3 \quad \alpha \beta=a+b \\ & \alpha+\beta=a \\ & \alpha^2-a \alpha=-(a+b) \\ & \beta^2-a \alpha=-(a+b) \\ &-\frac{1}{a+b}-\frac{1}{a+b}+\frac{2}{a+b}=0 \end{aligned} \]
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 \(\Delta(x)=\left|\begin{array}{ccc}x-2 & (x-1)^2 & x^3 \\ x-1 & x^2 & (x+1)^3 \\ x & (x+1)^2 & (x+2)^3\end{array}\right|\), then coefficient of \(x\) in \(\Delta(x)\) isWBJEE 2022 Medium
- Let \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) be real numbers, each greater than 1 , such that \(\frac{2}{3} \log _{\mathrm{b}} \mathrm{a}+\frac{3}{5} \log _{\mathrm{c}} \mathrm{b}+\frac{5}{2} \log _{\mathrm{a}} \mathrm{c}=3\). If the value of \(b\) is 9 , then the value of ' \(a\) ' must beWBJEE 2021 Easy
- If [a] denote the greatest integer which is less than or equal to a. Then, the value of the integral \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}[\sin x \cos x] d x\) isWBJEE 2013 Medium
- If \(\cos \theta+i \sin \theta, \theta \in \mathbb{R}\), is the root of the equation
\(a_0 x^n+a_1 \cdot x^{n-1}+\ldots .+a_{n-1} x+a_n=0, a_0, a_1, \ldots \ldots . a_n \in \mathbb{R}, a_0 \neq 0\)
then the value of \(a_1 \sin \theta+a_2 \sin 2 \theta+\ldots .+a_n \sin n \theta\) isWBJEE 2024 Medium - Let \(f: R \rightarrow R\) be a continuous function which satisfies \(f(x)=\int_{0}^{x} f(t) d t .\) Then. the value of \(f\left(\log _{e} 5\right)\) isWBJEE 2015 Medium
- The number of onto functions from the set \(\{1,2, \ldots, 11\}\) to the set \(\{1,2, \ldots, 10\}\) isWBJEE 2013 Easy
More PYQs from WBJEE
- An urn contains 8 red and 5 white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn isWBJEE 2012 Easy
- A \(100\) mL, \(0.1=\mathrm{M}\) solution of ammonium acetate is diluted by adding \(100 \mathrm{mL}\) of water. The pH of the resulting solution will be \(\left(p K_{a}\right.\) of acetic acid is nearly equal to \(\mathrm{pK}_{b}\) of \(\mathrm{NH}_{4} \mathrm{OH}\) )WBJEE 2012 Medium
- Let \(f(x)=\cos \left(\frac{\pi}{x}\right), x \neq 0,\) then assuming \(k\) as an integer,WBJEE 2018 Medium
- If \(f(x)=\frac{e^x}{1+e^x}, l_1=\int_{f(-a)}^{f(a)} x g(x(1-x)) d x\) and \(l_2=\int_{f(-a)}^{f(a)} g(x(1-x)) d x\), then the value of \(\frac{l_2}{l_1}\) isWBJEE 2024 Medium
- A given quantity of gas is taken from \(A\) to \(C\) in two ways; \(a\) ) directly from \(A \rightarrow C\) along a straight line and \(b\) ) in two steps, from \(A \rightarrow B\) and then from \(B \rightarrow C\). Work done and heat absorbed along the direct path \(A \rightarrow C\) is \(200 \mathrm{~J}\) and \(280 \mathrm{~J}\) respectively
WBJEE 2023 Easy - \(A\) train is moving with a uniform speed \(c^{2}\) \(33 \mathrm{m} / \mathrm{s}\) and an observer is approaching the train with the same speed. If the train blows a whistle of frequency \(1000 \mathrm{Hz}\) and the velocity of sound is \(333 \mathrm{m} / \mathrm{s},\) then the apparent frequency of the sound that the observer hears isWBJEE 2015 Medium