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State whether the following quadratic equations have two distinct real roots. Justify your answer. 2x2-32x+12 = 0 - Mathematics

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Sum

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

`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2)` = 0

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Solution

The equation `sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2)` = 0 has two real and distinct roots.

D = b2 – 4ac

= `(-3/sqrt(2))^2 - 4(sqrt(2))(1/2)`

= `(9/2) - 2sqrt(2) > 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.(vii) | Page 38
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