#### Question

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

(x - 2a)(x - 2b) = 4ab

#### Solution

The given equation is

(x - 2a)(x - 2b) = 4ab

x^{2} - 2bx - 2ax + 4ab = 4ab

x^{2} - 2bx - 2ax + 4ab - 4ab = 0

x^{2} - 2bx - 2ax = 0

x^{2} - 2(a + b)x = 0

The given equation is of the form of ax^{2} + bx + c = 0

where a = 1, b = 2(a + b), c = 0

Therefore, the discriminant

D = b^{2} - 4ac

= (2(a + b))^{2} - 4 x (1) x (0)

= 4(a + b)^{2}

= 4(a^{2} + b2 + 2ab)

= 4a^{2} + 4b2 + 8ab

∵ D > 0

∴ The roots of the given equation are real and distinct.

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#### APPEARS IN

Solution Determine the Nature of the Roots of the Following Quadratic Equation: (X - 2a)(X - 2b) = 4ab Concept: Nature of Roots.