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Question
Without solving, comment upon the nature of roots of the following equation:
x2 – ax – b2 = 0
Solution
x2 – ax – b2 = 0
a = 1, b = –a and c = –b2
∴ Discriminant = b2 – 4ac
= (–a)2 – 4(1)(–b2)
= a2 + 4b2
= a positive value
Since a2 + 4b2 is not a perfect square, roots are irrational
Since D > 0, then equation has two real and unequal roots.
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