Q. 13

# Prove that both t

For a quadratic equation, ax2 + bx + c = 0,

D = b2 – 4ac

If D > 0, roots are real.

x2 – (a + b)x + ab + x2 – (b + c)x + bc + x2 – (a + c)x + ac = 0

3x2 - 2(a + b + c)x + ab + bc + ac = 0

D = 4(a + b + c)2 – 12(ab + bc + ac)

D = a2 + b2 + c2 + 2ab + 2ac + 2bc – 3ab – 3bc – 3ac

D = 1/2 × (2a2 + 2b2 + 2c2 - 2ab – 2ac – 2bc)

D = 1/2 × ((a – b)2 + (b – c)2 + (c – a)2)

Thus, D is always greater than 0, and the roots are real

Now, when a = b = c,

D = 0, thus the roots are equal when a = b = c.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Introduction to Linear Equations in Two Variables62 mins
Pair of Linear Equations-Yahaan se laye marks57 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses