Question

If f ( x ) =ax^2 + bx + c, and f(1)=0 and f(-1) , then find the value of a+c

Answer 1

Answer:

given f(x) = ax^2 + bx + c

(i) put x=1 , f(1) = a+b+c

but given that f(1) = 8 hence a+b+c = 8——————-(1)

(ii) put x=-1 , f(-1) = a-b+c

but given that f(-1) = 4 hence a-b+c = 4——————-(2)

consider (1) + (2) :- a+b+c + a-b+c = 8 + 4

2a + 2c = 12

2(a+c) =12

a+c = 6.

HOPE IT HELPS ...............