JAMB - Mathematics (1984 - No. 22)
The quadratic equation whose roots are 1 - \(\sqrt{13}\) and 1 + \(\sqrt{13}\) is?
x2 + (1 - \(\sqrt{13}\)x + 1 + \(\sqrt{13}\) = 0
x2 - 2x - 12 = 0
x2 - 2x + 12 = 0
x2 + 12 + 2x2 = 0
Explanation
1 - \(\sqrt{13}\) and 1 + \(\sqrt{13}\)
sum of roots - \(1 + \sqrt{13} + 1 - \sqrt{13} = 2\)
Product of roots = (1 - \(\sqrt{13}\)) (1 + \(\sqrt{13}\)) = -12
x2 - (sum of roots) x + (product of roots) = 0
x2 - 2x - 12 = 0
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