For the quadratic $2 x^{2} - 7 x + 3 = 0$ , determine the nature of its roots.

medium 1 mark Class 10 · Mathematics · Quadratic Equations

Answer

Real and distinct roots

The correct answer is Real and distinct roots — Therefore the nature of the roots is real and distinct.

Step-by-step solution

Identify coefficients: $a = 2$ , $b = - 7$ , $c = 3$ .
Compute discriminant $D = b^{2} - 4 a c = (- 7)^{2} - 4 (2) (3) = 49 - 24 = 25$ .
Since $D > 0$ , the quadratic has two real and distinct roots.
Therefore the nature of the roots is real and distinct.

Common mistake: Using

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instead of

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when comparing the discriminant

Concept tested: Discriminant and nature of roots