Determine the nature of roots
root 3x square+2root2x minus 2 root 3=0
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Answer:
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.
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