The quadratic equation has _______ roots.

OR

The pair of linear equations 2x + 4y = 3 and 12y + 6x = 6 has/have _______ solutions/s.

The discriminant value of a quadratic equation ax² + bx + c = 0, a ≠ 0 is given by,

D = b² – 4ac = 0

Given,

⸫ D = b² – 4ac

⇒ D = (– √5)² – 4(2)(1)

⇒ D = – 3

Here, D < 0

Hence, the roots of the quadratic equation are imaginary.

OR

Given pair of equations are,

2x + 4y – 3 = 0 and 6x + 12y – 6 = 0

Here, a₁ = 2, b₁ = 4, c₁ = – 3

And a₂ = 6, b₂ = 12, c₂ = – 6

Here,

Hence, the given pair of linear equations has no solution.