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