Which of the following describes the nature of the roots of the quadratic equation 4x² - 7√3x + 12 = 0?

Question

Question

This question was previously asked in

RRB Group D 13 Sept 2022 Shift 2 Official Paper

Answer 1

Given:

4x² - 7√3x + 12 = 0

Formula and Concept used:

To find the roots of the quadratic equation, we need to find the discriminant (D),

For equation, \(ax^2+bx+c=0\) :

\(D=b^2-4ac\)

If D > 0, the equation has 2 real and different roots.

If D < 0, the equation has 2 complex roots (i.e. no real roots).

If D = 0, the equation has only 1 real root (or say 2 equal roots).

Calculation:

\(D=b^2-4ac \)

\(=({7 \sqrt3} )^2-4 × 4 × 12\)

\(=147-192\)

\(=-45\)

As D = - 45, i.e. < 0, the equation will have 2 distinct complex roots.

Hence, the quadratic equation '4x2 - 7√3x + 12 = 0' has no real roots.