Question:
If the roots of $4k^2 - (5k + 1)x + 5k = 0$ differ by unity then the sum of all possible values of k is
If the roots of $4k^2 - (5k + 1)x + 5k = 0$ differ by unity then the sum of all possible values of k is
Updated On: Jun 23, 2023
- $\frac{11}{5}$
- $\frac{12}{5}$
- $\frac{13}{5}$
- $\frac{14}{5}$
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Answer (d) $\frac{14}{5}$
Was this answer helpful?
0
0
Top Questions on Quadratic Equations
- The roots of the quadratic equation \(x^2 + x – p (p + 1) = 0 \)are :
- CBSE Class X - 2024
- Mathematics
- Quadratic Equations
- If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = 6x^2 + 11x - 10$, find the value of $\frac{\alpha}{\beta} + \frac{\beta}{\alpha}$.
- CBSE Class X - 2024
- Mathematics
- Quadratic Equations
- If the roots of quadratic equation \(4x^2 - 5x + k = 0\) are real and equal, then value of \(k\) is:
- CBSE Class X - 2024
- Mathematics
- Quadratic Equations
- If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = 6x^2 + 11x - 10$, find the value of $\frac{\alpha}{\beta} + \frac{\beta}{\alpha}$.
- CBSE Class X - 2024
- Mathematics
- Quadratic Equations
- The roots of the quadratic equation \(x^2 + x – p (p + 1) = 0 \)are :
- CBSE Class X - 2024
- Mathematics
- Quadratic Equations
View More Questions
Questions Asked in UPSEE exam
- A carnot engine takes 300 calories of heat at 500 K and rejects 150 calories of heat to the sink. The temperature of the sink is
- UPSEE - 2019
- Heat Transfer
- Which of the following is not permissible arrangement of electrons in an atom.
- UPSEE - 2019
- Quantum Mechanical Model of Atom
- If det $\begin{bmatrix}1&1&2\\ 2&4&9\\ t&t^{2}&1+t^{3}\end{bmatrix} = 0 $ , then the values of t are
- UPSEE - 2019
- Properties of Determinants
- The imaginary part of $\left( \frac{1}{2} + \frac{1}{2}i\right)^{10} $ is
- UPSEE - 2019
- Complex Numbers and Quadratic Equations
- Let S be the set of all right angled triangles with integer sides forming consecutive terms of an arithmetic progression. The number of triangles in S with perimeter less than 30 is
- UPSEE - 2019
- Arithmetic Progression
View More Questions
Concepts Used:
Quadratic Equations
A polynomial that has two roots or is of degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b, and c are the real numbers.
Consider the following equation ax²+bx+c=0, where a≠0 and a, b, and c are real coefficients.
The solution of a quadratic equation can be found using the formula, x=((-b±√(b²-4ac))/2a)
Two important points to keep in mind are:
- A polynomial equation has at least one root.
- A polynomial equation of degree ‘n’ has ‘n’ roots.
Read More: Nature of Roots of Quadratic Equation
There are basically four methods of solving quadratic equations. They are:
- Factoring
- Completing the square
- Using Quadratic Formula
- Taking the square root