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State whether the following quadratic equations have two distinct real roots. Justify your answer. (x + 1)(x – 2) + x = 0 - Mathematics

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Sum

State whether the following quadratic equations have two distinct real roots. Justify your answer.

(x + 1)(x – 2) + x = 0

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Solution

The equation (x + 1)(x – 2) + x = 0 has two real and distinct roots.

Simplifying the above equation,

x2 + x – 2x – 2 + x = 0

x2 – 2 = 0

D = b2 – 4ac

= (0)2 – 4(1)(–2)

= 0 + 8 > 0

Hence, the roots are real and distinct.

Concept: Nature of Roots
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APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.2 | Q 1.(x) | Page 38
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