The nature of the roots of quadratic equation $12 x^{2} - 4 \sqrt{15} x + 5 = 0$ is

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Real and equal

Real and unequal

None of these

Imaginary and unequal

answer is B.

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Detailed Solution

Given quadratic equation is,

12 x^{2} - 4 \sqrt{15} x + 5 = 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

12 x^{2} - 4 \sqrt{15} x + 5 = 0

we get,

a = 12, b = - 4 \sqrt{15}, c = 5

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

D = b^{2} - 4 ac

⟹ D = {(- 4 \sqrt{15})}^{2} - 4 \times 12 \times 5

⟹ D = 240 - 240

⟹ D = 0

The discriminant of the given equation is equal to zero.
This means the roots are real and equal.
Hence, the correct option is 2.

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