What is linear in 4x2 3x - 6?

Answer 1

4x2 + 3x - 6 is a second degree polynomial. Since the polynomial function f(x) = 4x2 + 3x - 6 has 2 zeros, it has 2 linear factors.

Since we cannot factor the given polynomial, let's find the two roots of the equation 4x2 + 3x - 6 = 0, which are the zeros of the function.

4x2 + 3x - 6 = 0

x2 + (3/4)x = 6/4

x2 + (3/4)x + (3/8)2 = 6/4 + 9/64

(x + 3/8)2 = 105/64

x + 3/8 = ± √(105/64)

x = (-3 ± √105)/8

x = -(3 - √105)/8 or x = -(3 + √105)/8

Thus, the linear factorization of f(x) = 4[x + (3 - √105)/8][x + (3 + √105)/8].