Question

has :
The quadratic equation 4x2+4root3x + 3 = 0
(a) two distinct real roots
(b) two equal real roots
(c) no real roots
(d) more than 2 real roots

Answer 1

Answer:

$4x {}^{2} + 4 \sqrt{3} x + 3 = 0$

$b {}^{2} - 4ac = (4 \sqrt{3} ) {}^{2} - 4(4)(3)$

$48 - 48 = 0$

Therefore the answer is two equal and real roots.

Answer 2

A quadratic equation with real coefficients can have either one or two distinct real roots, or two distinct complex roots. In this case the discriminant determines the number and nature of the roots. There are three cases: If the discriminant is positive, then there are two distinct roots.