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Determine the nature of roots of the following quadratic equations. 

i. x2 – 4x + 4 = 0 

ii. 2y2 – 7y + 2 = 0 

iii. m2 + 2m + 9 = 0

1 Answer

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i. x2 – 4x + 4= 0 

Comparing the above equation with

ax2 + bx + c = 0, we get

a = 1, b = -4, c = 4

∴ ∆ = b2 – 4ac 

= (- 4)2 – 4 × 1 × 4 

= 16 – 16 

∴ ∆ = 0

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

ii. 2y2 – 7y + 2 = 0

Comparing the above equation with

ay2 + by + c = 0, we get

a = 2, b = -7, c = 2

∴ ∆ = b2 – 4ac 

= (- 7)2 – 4 × 2 × 2 

= 49 – 16 

∴ ∆ = 33 

∴ ∆ > 0

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

iii. m2 + 2m + 9 = 0

Comparing the above equation with

am2 + bm + c = 0, we get 

a = 1, b = 2, c = 9 

∴ ∆ = b2 – 4ac 

= (2)2 – 4 × 1 × 9

= 4 – 36 

∴ ∆ = -32 

∴ ∆ < 0

∴ Roots of the given quadratic equation are not real.

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