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Question
Without solving, comment upon the nature of roots of the following equation:
`x^2 + 2sqrt(3)x - 9 = 0`
Solution
`x^2 + 2sqrt(3)x - 9 = 0`
a = 1, b = `2sqrt(3)` and c = −9
∴ Discriminant = b2 – 4ac
= `(2sqrt3)^2 - 4(1) (-9)`
= 12 + 36
= 48
Since 48 is not a perfect square, roots are irrational
Since D > 0, then equation has two real and unequal roots.
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