Mathematics

Without solving, comment upon the nature of roots of the following equation :

x2 - ax - b2 = 0

Quadratic Equations

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Answer

Comparing x2 - ax - b2 = 0 with ax2 + bx + c = 0 we get,

a = 1, b = -a and c = -b2.

We know that,

Discriminant = D = b2 - 4ac = (-a)2 - 4(1)(-b2)

= a2 + 4b2; which is positive.

Since, a, b and c are real numbers; a ≠ 0 and b2 - 4ac > 0

∴ The roots are real and unequal.

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