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(1) \(x^2\) – 4\(x\) + 4 = 0.

(2) 2\(y^2\) – 7y + 2 = 0

(3) \(m^2\) + 2m + 9 = 0

Print or Save(1) \(x^2\) – 4\(x\) + 4 = 0.

Sol. \(x^2\) – 4\(x\) + 4 = 0. comparing with a\(x^2\) + b\(x\) + c = 0

We get, a = 1 b = –4 c = 4

∴ \(b^2\) – 4ac = \((-4)^2\) – 4 × 1 × 4

∴ Δ = 16 – 16

∴ Δ = 0

∴ \(b^2\) – 4ac = 0

∴ **The roots of the equation are real and equal.**

(2) 2\(y^2\) – 7y + 2 = 0

Sol. 2\(y^2\) – 7y + 2 = 0 comparing with a\(x^2\) + b\(x\) + c = 0

We get, a = 2, b = –7 and c = 2

\(b^2\) – 4ac = \((-7)^2\) – 4 × 2 × 2

∴ Δ = 49 – 16

∴ Δ = 33

∴ \(b^2\) – 4ac > 0

∴ **The roots of equation are real and unequal.**

(3) \(m^2\) + 2m + 9 = 0

Sol. \(m^2\) + 2m + 9 = 0 comparing with a\(x^2\) + b\(x\) + c = 0

a = 1 b = 2 and c = 9

\(b^2\) – 4ac = \(2^2\) – 4 × 1 × 9

∴ Δ = 4 – 36

∴ Δ = –32

∴ b2 – 4ac < 0

∴ **The roots of equation are not real.**