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Question
Determine the nature of the roots of the following quadratic equation:
2(a2 + b2)x2 + 2(a + b)x + 1 = 0
Solution
The given equation is
2(a2 + b2)x2 + 2(a + b)x + 1 = 0
The given equation is in the form of ax2 + bx + c = 0
where a = 2(a2 + b2), b = 2(a + b), c = 1
Therefore the discriminant
D = b2 - 4ac
= (2(a + b))2 - 4 x (2(a2 + b2)) x (1)
= 4(a + b)2 - 8a2 - 8b2
= 4(a2 + b2 + 2ab) - 8a2 - 8b2
= 4a2 + 4b2 + 8ab - 8a2 - 8b2
= 8ab - 4a2 - 4b2
∵ D < 0,
∴ The roots of the given equation are not real.
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