Given f(x) = 2x²+8x-24
One way to find the zeros of this function is by factorizing
Find a pair of numbers that multiplied give the same answer as (2 × -24) and the same pair of numbers must add up to 8 → The value 2, -24, and 8 are the coefficients of the given function
The pair of numbers are 12 and -4
Then we write
f(x) = 2x² + 12x - 4x - 24
f(x) = (2x² + 12x) - (4x + 24)
f(x) = (2x(x+6)) - (4(x+6)) → There's a common factor (x+6)
f(x) = (x + 6)(2x - 4)
f(x) = 0
(x + 6)(2x - 4) = 0
x + 6 = 0 OR 2x - 4 =0
x = -6 OR x = 4/2 = 2
The positive zero is x = 2 and it comes from (2x - 4)
Answer: Option C
