JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(2\) and \(6\) are the roots of the equation \(a x^2+b x+1=0\), then the quadratic equation, whose roots are \(\frac{1}{2 a+b}\) and \(\frac{1}{6 a+b}\), is :
- A \(2 x^2+11 x+12=0\)
- B \(4 x^2+14 x+12=0\)
- C \(x^2+10 x+16=0\)
- D \(x^2+8 x+12=0\)
Answer & Solution
Correct Answer
(D) \(x^2+8 x+12=0\)
Step-by-step Solution
Detailed explanation
Sum \(=8=-\frac{b}{a} \) Product \(=12=\frac{1}{a} \quad \Rightarrow a=\frac{1}{12} \) \( b=-\frac{2}{3} \) \( 2 a+b=\frac{2}{12}-\frac{2}{3}=-\frac{1}{2} \) \( 6 a+b=\frac{6}{12}-\frac{2}{3}=-\frac{1}{6} \) sum \(=-8 \) \( P=12 \) \( x^2+8 x+12=0\)
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
- The variance of the numbers \(8,21,34,47, \ldots, 320\) isJEE Mains 2025 Easy
- Let \(l_{1}\) be the line in \(xy\)-plane with \(x\) and \(y\) intercepts \(\frac{1}{8}\) and \(\frac{1}{4 \sqrt{2}}\) respectively, and \(l_{2}\) be the line in \(zx\)-plane with \(x\) and \(z\) intercepts \(-\frac{1}{8}\) and \(-\frac{1}{6 \sqrt{3}}\) respectively. If \(d\) is the shortest distance between the line \(l_{1}\) and \(l_{2}\), then \(d ^{-2}\) is equal toJEE Mains 2022 Hard
- Let \(A\) be any \(3 \times 3\) invertible matrix. Then which one of the following is not always true ?JEE Mains 2017 Hard
- The value of \(\frac{1 \times 2^2+2 \times 3^2+\ldots+100 \times(101)^2}{1^2 \times 2+2^2 \times 3+\ldots+100^2 \times 101}\) isJEE Mains 2024 Hard
- Let \(L_{1}\) be a tangent to the parabola \(y ^{2}=4( x +1)\) and \(L _{2}\) be a tangent to the parabola \(y ^{2}=8( x +2)\) such that \(L _{1}\) and \(L _{2}\) intersect at right angles. Then \(L_{1}\) and \(L_{2}\) meet on the straight lineJEE Mains 2020 Hard
- The equation \(\left| {z - i} \right| = \left| {z - 1} \right|,i = \sqrt { - 1} \), representsJEE Mains 2019 Hard
More PYQs from JEE Mains
- Let \(S=\{1,2,3,4,5,6\} .\) Then the probability that a randomly chosen onto function \(\mathrm{g}\) from \(\mathrm{S}\) to \(\mathrm{S}\) satisfies \(g(3)=2 g(1)\) is :JEE Mains 2021 Medium
- Which of the following is not correct for relation \(\mathrm{R}\) on the set of real numbers ?JEE Mains 2021 Medium
- The locus of a point, which moves such that the sum of squares of its distances from the points \((0,0),(1,0),(0,1)(1,1)\) is \(18\) units, is a circle of diameter \(\mathrm{d}\). Then \(\mathrm{d}^{2}\) is equal to ...... .JEE Mains 2021 Medium
- If \(p, q, r\) are \(3\) real numbers satisfying the matrix equation, \([p\,q\,r]\,\left[ {\begin{array}{*{20}{c}}
3&4&1\\
3&2&3\\
2&0&2
\end{array}} \right] = [3\,\,\,0\,\,\,1]\) then \(2p + q - r\) equalsJEE Mains 2013 Hard - If tangents are drawn to the ellipse \(x^2 + 2y^2 = 2\) at all points on the ellipse other than its four vertices than the mid points of the tangents intercepted between the coordinate axes lie on the curveJEE Mains 2019 Hard
- If \(x =1\) is a critical point of the function \(f(x)=\left(3 x^{2}+a x-2-a\right) e^{x},\) thenJEE Mains 2020 Hard