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Determine the Nature of the Roots of the Following Quadratic Equation: 9a2b2x2 - 24abcdx + 16c2d2 = 0 - Mathematics

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Question

Determine the nature of the roots of the following quadratic equation:

9a2b2x2 - 24abcdx + 16c2d2 = 0

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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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.6 | Q: 15.2 | Page no. 42
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.6 | Q: 15.2 | Page no. 42
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Determine the Nature of the Roots of the Following Quadratic Equation: 9a2b2x2 - 24abcdx + 16c2d2 = 0 Concept: Nature of Roots.
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