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)
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-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.