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Without solving, examine the nature of roots of the equation x^2 – 5x – 2 = 0 - Mathematics

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Sum

Without solving, examine the nature of roots of the equation x2 – 5x – 2 = 0

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Solution

Comparing x2 – 5x – 2 = 0 with ax2 + bx + c = 0;

we get: a = 1, b = – 5 and c = – 2

D = b2 – 4ac = (–5)2 – 4 × 1 × – 2

= 25 + 8 = 33 ; which is positive but not a perfect square.

∴ The roots of the given equation are irrational and unequal

Concept: Nature of Roots
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