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

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Solution

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

Simplifying the above equation,

x2 – x + 2x – 2 + 2 = 0

x2 + x = 0

D = b2 – 4ac

= 12 – 4(1)(0)

= 1 – 0 > 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.(ix) | Page 38
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