CBSE Class 10 Answered
if a+b+c=0, show that the roots of eq. ax*x+bx+c=0 are rational
Asked by pulakananda | 18 Feb, 2011, 09:29: PM
Expert Answer
Dear Student,
Here is the solution:
Since a + b + c = 0 hence b = -(c + a)
The given quadratic equation is ax2 + bx + c = 0
Or ax2 –(c + a)x + c = 0 (1)
The discriminant of equation (1) is {-(c + a)}2 – 4ac = (c + a)2 – 4ac = (c - a) 2
Since a, b, c are rational and the discriminant of equation (1) is a perfect square, hence the roots of (1) are rational.
The given quadratic equation is ax2 + bx + c = 0
Or ax2 –(c + a)x + c = 0 (1)
The discriminant of equation (1) is {-(c + a)}2 – 4ac = (c + a)2 – 4ac = (c - a) 2
Since a, b, c are rational and the discriminant of equation (1) is a perfect square, hence the roots of (1) are rational.
Regards
Team Topperlearning.
Answered by | 23 Feb, 2011, 07:23: PM
Application Videos
-
Factorisation Method - 1
This video explains the concept of Factorisation Method to find the roots o... -
Completing Square Method
This video explains the concept of Completing Square Method to find the roo... -
Nature of Roots
This video explains the concept of Discriminant and Nature of Roots. -
Find the roots of a given Quadratic Equation by Formula ...
This video explains the concept of Formula Method to find the roots of a gi... -
Word problems in Quadratic equations
This video explains a case study based question on the concept of quadra...
Concept Videos
-
Introduction to Quadratic Equations ...
This video explains the definition of quadratic equation and solve the rela... -
Method of Completing the Square ...
This video explains the determination of roots of the quadratic equation by... -
Concept of discriminant to classify roots of quadratic ...
Understand the concept of discriminant to classify roots of quadratic equat... -
Word Problems in Quadratic Equations
This video covers word problems related to quadratic equations -
Introduction to Quadratic Equations
This video explains the definition of quadratic equation and solve the rela...
CBSE 10 - Maths
Asked by rrajansinghakb199 | 08 Apr, 2024, 05:12: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by afiyamallick12 | 23 Feb, 2024, 11:32: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by goyelgurav | 18 Dec, 2023, 11:23: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by mehraharshit.dk000 | 05 Oct, 2023, 08:05: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by ruchipandey20071978 | 21 May, 2023, 10:00: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by varma.renu9481 | 25 Jan, 2023, 04:11: PM
ANSWERED BY EXPERTCBSE 10 - Maths
Asked by yogitamanojkumar | 09 Jan, 2023, 04:01: PM
ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by nk.neetuhome | 18 Nov, 2022, 03:43: PM
ANSWERED BY EXPERT
