The nature of the roots of quadratic equation $5 x^{2} - 4 x + 1 = 0$ is

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Real and unequal

Real and equal

Imaginary and unequal

None of these

answer is C.

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Detailed Solution

Given quadratic equation is,

5 x^{2} - 4 x + 1 = 0

.
A quadratic equation in the variable x is of the form

a x^{2} + bx + c = 0, a \neq 0

where a, b and c are real numbers.
After comparing the given equation

5 x^{2} - 4 x + 1 = 0

, we get,

a = 5, b = - 4, c = 1

.
To find the nature of the roots we have the formula,

D = b^{2} - 4 ac

⟹ D = {(- 4)}^{2} - 4 \times 5 \times 1

⟹ D = 16 - 20

⟹ D = - 4 < 0

The discriminant of the given equation is less than zero.
This means the nature of the roots of the equation

5 x^{2} - 4 x + 1 = 0

are imaginary and unequal.
Hence, the correct option is 3.

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