If f(x) = ax2 + bx + c, f(− 7/3 )= 17/3 and f( 7/3 )=− 17/3 , then the ratio c to a is If f(x) = ax2 + bx + c, f(− 7/3 )= 17/3 and f( 7/3 )=− 17/3 , then the ratio c to a is ?

Question

If f(x) = ax2 + bx + c, f(− 7/3 )= 17/3 and f( 7/3 )=− 17/3 , then the ratio c to a is

If f(x) = ax2 + bx + c, f(− 7/3 )= 17/3 and f( 7/3 )=− 17/3 , then the ratio c to a is

?

Answer 1

f(-7/3) = 17/3 = a(-7/3)² + b(-7/3) + c ...(1)

f(7/3) = -17/3 = a(7/3)² + b(7/3) + c ...(2)

Cleaning up (1) yields: a(7/3)² - b(7/3) + c = 17/3 ...(3)

Now we are going to add (2) and (3)

a(7/3)² - b(7/3) + c = 17/3

+ a(7/3)² + b(7/3) + c = -17/3

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2a(7/3)² + 2c = 0

=> (7/3)² + c/a = 0 ...dividing both sides by 2a

=> c/a = -(7/3)² = -49/9