Sum

Without solving, examine the nature of roots of the equation 2x^{2} – 7x + 3 = 0

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#### Solution

Comparing 2x^{2} – 7x + 3 = 0 with ax^{2} + bx + c = 0;

we get: a = 2, b = – 7 and c = 3

D = b^{2} – 4ac = (–7)^{2} – 4 × 2 × 3

= 49 – 24 = 25, which is perfect square.

∴ The roots of the given equation are rational and unequal

Concept: Nature of Roots

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