Determine the nature of the roots of the equation $4 x^{2} - 4 x + 1 = 0$

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Solution

Consider the equation $4 x^{2} - 4 x + 1 = 0$
This is in the form of $a x^{2} + b x + c = 0$ . The co-efficient are $a = 4, b = - 4, c = 1$
$△ = b^{2} - 4 a c, △ (- 4)^{2} - 4 (4) (1), △ = 16 - 16$
$∴ △ = 0$ . Therefore, roots are real and equal

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