Find the point on the curve at which the tangent passes through the origin.

If tangent is pass through origin it means that equation of tangent is y = mx

Let us suppose that tangent is made at point (x₁, y₁)

y₁ = x₁² + 3x₁ + 4 …(1)

m at (x₁, y₁) = 2x₁ + 3

Equation of tangent : y₁ = (2x₁ + 3)x₁ …(2)

On compairing eq(1) and eq(2)

x₁² + 3x₁ + 4 = (2x₁ + 3)x₁

x₁² – 4 = 0 ⇒ x₁ = 2 and -2

At x₁ = 2, y₁ = 14

At x₁ = -2, y₁ = 2

So, required points are (2, 14) and (-2, 2)