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State whether the following quadratic equations have two distinct real roots. Justify your answer.
CBSE | Class 10 | Maths | NCERT Exemplar | Quadratic Equations
State whether the following quadratic equations have two distinct real roots. Justify your answer.
  1. √2 x2 –(3/√2)x + 1/√2 = 0
  2. x (1 – x) – 2 = 0

(vii)

The condition √2×2 – 3x/√2 + ½ = 0 has two genuine and unmistakable roots.

    \[\begin{array}{*{35}{l}} <!-- /wp:paragraph --> <!-- wp:paragraph --> D\text{ }=\text{ }b2\text{ }\text{ }4ac \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> ~ \\ <!-- /wp:paragraph --> <!-- wp:paragraph --> \end{array}\]

    \[=\text{ }\left( -\text{ }3/\surd 2 \right)2\text{ }\text{ }4\left( \surd 2 \right)\text{ }\left( {\scriptscriptstyle 1\!/\!{ }_2} \right)\]

= (9/2) – 2√2 > 0

Henceforth, the roots are genuine and particular.

(viii)

The condition x (1 – x) – 2 = 0 has no genuine roots.

Improving on the above condition,

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

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

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

= 1 – 8 < 0

Subsequently, the roots are fanciful.

i

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