Question:
If a,b,c are real numbers then the roots of
(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are always
If a,b,c are real numbers then the roots of
(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are always
Show Hint
Check discriminant to decide nature of roots.
Updated On: Mar 20, 2026
- real
- imaginary
- positive
- negative
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Simplify equation: 3x²-2(a+b+c)x+(ab+bc+ca)=0
Step 2: Discriminant: Δ=[2(a+b+c)]²-12(ab+bc+ca)\ge0
Was this answer helpful?
0
0
Top Questions on Quadratic Equations
- If \( \alpha,\beta \) where \( \alpha<\beta \), are the roots of the equation \[ \lambda x^2-(\lambda+3)x+3=0 \] such that \[ \frac{1}{\alpha}-\frac{1}{\beta}=\frac{1}{3}, \] then the sum of all possible values of \( \lambda \) is:
- JEE Main - 2026
- Mathematics
- Quadratic Equations
- If the arithmetic mean of \(\dfrac{1}{a}\) and \(\dfrac{1}{b}\) is \(\dfrac{5}{16}\) and \(a,\,4,\,\alpha,\,b\) are in increasing A.P., then both the roots of the equation \[ \alpha x^2-ax+2(\alpha-2b)=0 \] lie between:
- JEE Main - 2026
- Mathematics
- Quadratic Equations
- Let $\alpha, \beta$ be the roots of the quadratic equation \[ 12x^2 - 20x + 3\lambda = 0,\ \lambda \in \mathbb{Z}. \] If \[ \frac{1}{2} \le |\beta-\alpha| \le \frac{3}{2}, \] then the sum of all possible values of $\lambda$ is
- JEE Main - 2026
- Mathematics
- Quadratic Equations
- The roots of the quadratic equation $x^2 + 5x + 6 = 0$ will be :
- UP Board X - 2026
- Mathematics
- Quadratic Equations
- The sum of all the roots of the equation \((x-1)^2 - 5|x-1| + 6 = 0\), is:
- JEE Main - 2026
- Mathematics
- Quadratic Equations
View More Questions
Questions Asked in BITSAT exam
- The 5th term of an AP is 20 and the 12th term is 41. Find the first term.
- BITSAT - 2025
- Arithmetic Progression
- A dust particle of mass 4 × 10⁻¹² mg is suspended in air under the influence of an electric field of 50 N/C directed vertically upwards. How many electrons were removed from the neutral dust particle? (g = 10 m/s²)
- BITSAT - 2025
- Electrostatics
- Calculate the electric field at a point due to a uniformly charged spherical shell.
- BITSAT - 2025
- Electrostatics
- What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
- BITSAT - 2025
- Vector Algebra
- Calculate the de Broglie wavelength of an electron moving with a given velocity.
- BITSAT - 2025
- Wave Optics
View More Questions