Given that the line y = mx + 1 is the tangent to the parabola y² = 4x. We need to find the value of m.

Let us substitute the value in the equation of parabola.

⇒ (mx + 1)² = 4x

⇒ m²x² + 2mx + 1 = 4x

⇒ m²x² + (2m - 4)x + 1 = 0

The quadratic will have similar roots if the line is tangent to the parabola.

We know that for a quadratic equation ax² + bx + c = 0 to have equal roots, the condition to be satisfied is b² - 4ac = 0

⇒ (2m - 4)² - 4(m²)(1) = 0

⇒ 4m² - 16m + 16 - 4m² = 0

⇒ 16 - 16m = 0

⇒ 16m = 16

⇒ m = 1

∴The value of m is 1.