Question

(1) Determine the nature of the roots for the quadratic equation √3 x² + √2x - 2/3=0. ​

Answer 1

Answer:

We know that while finding the root of a quadratic equation ax2+bx+c=0 by quadratic formula x=2a−b±b2−4ac, 

if b2−4ac>0, then the roots are real and distinct 

if b2−4ac=0, then the roots are real and equal and

if b2−4ac<0, then the roots are imaginary.

Here, the given quadratic equation x2−2x+3=0 is in the form ax2+bx+c=0 where a=1,b=−2 and c=3, therefore,

  

b2−4ac=(−2)2−(4×1×3)=4−12=−8<0

Since b2−4ac<0   

Hence the roots are imaginary or no real roots.

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