Question

Determine the nature of roots for each of the quadratic equation.

i. 3x² – 5x + 7 = 0 

ii. √3 x² + √2 x – 2 √3 = 0 

iii. m² – 2m + 1 = 0

Answer 1

i. 3x² – 5x + 7 = 0

Comparing the above equation with

ax² + bx + c = 0, we get 

a = 3, b = -5, c = 7 

∴ ∆ = b² – 4ac 

= (-5)² -4 × 3 × 7 

= 25 – 84 

∴ ∆ = -59 

∴ ∆ < 0

∴ Roots of the given quadratic equation are not real.

ii. √3 x² + √2 x – 2 √3 = 0 

Comparing the above equation with 

ax² + bx + c = 0, we get 

a = √3 , b = √2, c = -2√3 

∴ ∆ = b² – 4ac 

= (√2)² – 4 × √3 × (-2√3)

= 2 + 24 

∴ ∆ = 26 

∴ ∆ > 0

∴ Roots of the given quadratic equation are real and unequal.

iii. m² – 2m + 1 = 0

Comparing the above equation with

am² + bm + c = 0, we get

a = 1, b = -2, c = 1 

∴ ∆ = b² – 4ac 

= (-2)² – 4 × 1 × 1 

= 4 – 4 

∴ ∆ = 0

∴ Roots of the given quadratic equation are real and equal.