Question

How do you this problem?

Answer 1

f(x) = ax^2 - 4x + b

If x = -2 , 3 are solutions of zeros function f(x) then b = ?

If x = -2 then a(-2)^2 - 4(-2) + b = 0

4a + 8 + b = 0 (1st)

If x = 3. then a(3)^2 - 4(3) + b = 0

9a - 12 + b = 0 (2nd)

Subtract (2nd) and (1st)

4a + 8 + b = 0 (1st)

9a - 12 + b = 0 (2nd)

--------------------------

-5a + 20 = 0

-5a = -20

a = 4

Substitute a = 4 into 4a + 8 + b = 0 (1st)

4(4) + 8 + b = 0

16 + 8 = -b

b = -24

Answer is A) -24

Double check:

a = 4 and b = -24 so

f(x) = 4x^2 - 4x - 24

zero function:

4x^2 - 4x - 24 = 0

4(x^2 - x - 6) = 0

4(x - 3)(x + 2) = 0

x - 3= 0; x = 3

x = -2 = 0; x = -2

x = -2 , 3 are solutions of the function.