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Nature of the root can be identified by D=b^2-4ac If it is -ve then root will imaginary If it is +ve then root will be real and different If it is equal to Zero, then both root will be real and equal 1) 6x^2-x - 2=0 ax^2+bx+c=o on comparing , we will find D 1-4*6*-2= -ve then root will be imaginary 2) x^2+x+1=0 D= 1 -4*1*1 = -ve,then rootwill be imaginary 3) 2x^2+5x+5=0 D= 25-4*2*5= -ve, root will be imaginary

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We use discriminant for this purpose for the equation ax² + bx + c = 0

D = b² - 4ac

If D > 0 roots are real and distinct D < 0 roots are imaginary and distinct D = 0 Roots are real and equal

so 1) 6x² - x - 2 = 0 D = (-1²) - 4 x 6 x - 2 D = 1 + 48 = 49 So D > 0 roots are real and distinct

2) x² - 2x + 1 = 0 D = (- 2)² - 4 x 1 x 1 D = 4 - 4 = 0 So D = 0 Roots are real and equal

3) x² + x + 1 = 0 D = 1² - 4 x 1 x 1 = 1 - 4 = - 3 So D < 0 roots are imaginary and distinct

4) 2x² + 5x + 5 = 0 D = 5² - 4 x 5 x 2 = 25 - 40 = - 15 So D < 0 roots are imaginary and distinct