Question

The roots of the equation $3x^2-4x+3=0$ are :

• A. real and unequal
• B. real and equal
• C. imaginary
• D. none of these

Answer 1

The correct option is C imaginary

Given equation is $3x^2-4x+3=0$

To find, the nature of the roots of the equation

An equation is said to have

(i) two distinct and real roots if the discriminant $b^2-4ac>0$

(ii) equal real roots if $b^2-4ac=0$

(iii) no real roots or imaginary roots if $b^2-4ac<0$

In the given equation $a=3,b=-4,c=3$

Hence the discriminant is $(-4{)}^2-4(3\left)\right(3)=16-36=-20<0$

Therefore the roots of the given equation are imaginary in nature.