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04 Jul 2023, 03:45
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If function f(x) = (x - a)(x - b) and f(10) = f(20) = 0, what is the value of f(30) ?
A. 50
B. 100
C. 150
D. 200
E. 250
A. 50
B. 100
C. 150
D. 200
E. 250
04 Jul 2023, 03:53
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Since f(10) = f(20) = 0, a and b must be 10 and 20 (not necessarily in that order).
So f(x) = (x-10)(x-20)
f(30) = 20*10 = 200
Option D is answer.
So f(x) = (x-10)(x-20)
f(30) = 20*10 = 200
Option D is answer.
Bunuel
04 Jul 2023, 04:05
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If function f(x) = (x - a)(x - b) and f(10) = f(20) = 0, what is the value of f(30) ?
A. 50
B. 100
C. 150
D. 200
E. 250
f(x) = (x - a)(x - b)
f(10) = (10 - a)(10 - b) = 100 - 10(a+b) + ab = 0 ------------ a)
f(20) = (20 - a)(20 - b) = 400 - 20(a+b) + ab = 0 ------------ b)
f(30) = (30 - a)(30 - b) = 900 - 30(a+b) + ab ------------ c)
from a,b
30(a+b) = 500 + 2ab ------------ d)
substitute d in c
900 - 500 - 2ab + ab => 400 - ab ------------e)
Now 2*a - b
200 - 20(a+b) + 2ab - 400 + 20(a+b) -ab = -200 + ab = 0
so ab = 200------------------f)
substitute f in e.
400 - 200 = f(30) = 200
A. 50
B. 100
C. 150
D. 200
E. 250
f(x) = (x - a)(x - b)
f(10) = (10 - a)(10 - b) = 100 - 10(a+b) + ab = 0 ------------ a)
f(20) = (20 - a)(20 - b) = 400 - 20(a+b) + ab = 0 ------------ b)
f(30) = (30 - a)(30 - b) = 900 - 30(a+b) + ab ------------ c)
from a,b
30(a+b) = 500 + 2ab ------------ d)
substitute d in c
900 - 500 - 2ab + ab => 400 - ab ------------e)
Now 2*a - b
200 - 20(a+b) + 2ab - 400 + 20(a+b) -ab = -200 + ab = 0
so ab = 200------------------f)
substitute f in e.
400 - 200 = f(30) = 200
