What should a be so that a⋅x² + 2x + 4 has the value 5 at x=1?

Given: a⋅x² + 2x + 4, find a such that the expression equals 5 when x = 1.

Substitute x with 1: a⋅(1)² + 2⋅(1) + 4 = 5

Simplify the squares and multiplications: a⋅1 + 2 + 4 = 5

Since 1 squared is 1 and a times 1 is a: a + 2 + 4 = 5

Combine like terms (2 + 4): a + 6 = 5

Subtract 6 from both sides to solve for a: a = 5 – 6

Calculate the difference: a = -1

Therefore, the value of a must be -1.