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Home »  State whether the following quadratic equations have two distinct real roots. Justify your answer.
 State whether the following quadratic equations have two distinct real roots. Justify your answer.
CBSE | Class 10 | Exercise 4.2 | Maths | NCERT Exemplar | Quadratic Equations
 State whether the following quadratic equations have two distinct real roots. Justify your answer.
  1. (x – 1) (x + 2) + 2 = 0
  2. (x + 1) (x – 2) + x = 0

(ix)

The condition (x – 1) (x + 2) + 2 = 0 has two genuine and unmistakable roots.

Working on the above condition,

    \[x2\text{ }\text{ }x\text{ }+\text{ }2x\text{ }\text{ }2\text{ }+\text{ }2\text{ }=\text{ }0\]

    \[x2\text{ }+\text{ }x\text{ }=\text{ }0\]

    \[D\text{ }=\text{ }b2\text{ }\text{ }4ac\]

    \[=\text{ }12\text{ }\text{ }4\left( 1 \right)\left( 0 \right)\]

= 1 – 0 > 0

Thus, the roots are genuine and unmistakable.

(x)

The condition (x + 1) (x – 2) + x = 0 has two genuine and particular roots.

Improving on the above condition,

    \[x2\text{ }+\text{ }x\text{ }\text{ }2x\text{ }\text{ }2\text{ }+\text{ }x\text{ }=\text{ }0\]

    \[x2\text{ }\text{ }2\text{ }=\text{ }0\]

    \[D\text{ }=\text{ }b2\text{ }\text{ }4ac\]

    \[=\text{ }\left( 0 \right)2\text{ }\text{ }4\left( 1 \right)\text{ }\left( -\text{ }2 \right)\]

= 0 + 8 > 0

Thus, the roots are genuine and unmistakable.

i

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