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

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

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

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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.

Concept: Nature of Roots
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.6 | Q 15.4 | Page 42
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