Advertisement Remove all ads

Determine the Nature of the Roots of the Following Quadratic Equation: (B + C)X2 - (A + B + C)X + a = 0 - Mathematics

Determine the nature of the roots of the following quadratic equation:

(b + c)x2 - (a + b + c)x + a = 0

Advertisement Remove all ads

Solution

The given equation is (b + c)x2 - (a + b + c)x + a = 0

The given equation is in the form of ax2 + bx + c = 0

where a = (b + c), b = -(a + b + c), c = a

Therefore, the discriminant

D = b2 - 4ac

= (-(a + b + c))2 - 4 x (b + c) x (a)

= (a + b + c)2 - 4ab - 4ac

= a2 + b2 + c2 + 2ab + 2bc + 2ca - 4ab - 4ac

= a2 + b2 + c2 - 2ab + 2bc - 2ac

∵ D > 0

∴ The roots of the given equation are real and distonct.

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.6 | Q 15.4 | Page 42
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×