Question

Determine the nature of roots of the following equations from their discriminant.
y² – 5y + 11 = 0

Answer 1

Given: y² – 5y + 11 = 0
To find the nature of the roots, we need to find the discriminant of the given quadratic equation.
We know that the discriminant of a quadratic equation is Δ =b² – 4ac.
On comparing the given equation with ay² + by + c = 0 in variable y, we get:
a = 1, b = –5 and c = 11
Thus,
Δ = (–5)² – 4(1)(11)
=> Δ = 25 – 44 = –19
Since Δ < 0, the roots of the given quadratic equation are not real.