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

Solution

## The correct option is C imaginaryGiven equation is $$3x^2-4x+3=0$$To find, the nature of the roots of the equationAn 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 $$(-4)^2-4(3)(3)=16-36=-20<0$$Therefore the roots of the given equation are imaginary in nature.Mathematics

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