The coordinates of the point on the curve $y=x^2+3 x+4$ the tangent at which passes through the origin is equal to

(2, 14), (–2, 2)

$\frac{d y}{d x}=2 x+3$

∴ equation of tangent is Y - y = (2x + 3)(X - x)

It passes through (0, 0),   ∴  -y = -x(2x + 3)

$\Rightarrow y=x(2 x+3) \Rightarrow 2 x^2+3 x=x^2+3 x+4$

⇒ x = 2, –2; y = 14, –2.