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Nature of Roots

y2+6 y+9=0

Question

y² + 6y + 9 = 0

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Solution

Given: y² + 6y + 9 = 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 = 6 and c = 9.
Thus,
Δ = (6)² – 4(1)(9)
=> Δ = 36 – 36 = 0
Since Δ = 0, the roots of the given quadratic equation are real and equal.

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