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Question

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


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

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 $$(-4)^2-4(3)(3)=16-36=-20<0$$
Therefore the roots of the given equation are imaginary in nature.

Mathematics

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