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Question
Determine the nature of the roots of the following quadratic equation:
9a2b2x2 - 24abcdx + 16c2d2 = 0
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Solution
The given equation is
9a2b2x2 - 24abcdx + 16c2d2 = 0
The given equation is on the form of ax2 + bx + c = 0
where a = 9a2b2, b = -24abcd, c = 16c2d2
Therefore, the discriminant
D = b2 - 4ac
= (-24abcd)2 - 4 x (9a2b2) x (16c2d2)
= 576a2b2c2d2 - 576a2b2c2d2
= 0
∵ D = 0
∴ The roots of the given equation are real and equal.
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