Question

3x2 -4√3x+4=0 find nature of roots and give roots of quadratic equation

Answer 1

Answer:

Nature of Roots: Real and Equal roots

Step-by-step explanation:

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

On comparing with general quadratic equation $ax^2+bx+c=0$,

$a=3\\b=-4\sqrt{3} \\c=4$

The nature of a quadratic equation is given by discriminant,

where Discriminant, $D=b^2-4ac$

If $D>0$, then Real and Distinct Roots,

If $D=0$, then Real and Equal Roots, &

If $D<0$, then Imaginary Roots.

for the given equation

$D=(-4\sqrt{3} )^2-4(3)(4)=16\times 3-48=48-48=0$,

As $D=0$

Thus, Real and Equal Roots.