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.