Given that fx is a cubic function with zeros at 70 and 4 fin

Given that f(x) is a cubic function with zeros at -7,0, and 4, find an equation for f(x) given that f(7)= -3.   f(x)= ?

Solution

Let f( x ) = a(x+7)(x - 0)( x -4) + b . Since f (x) has a zero at 0, we have f( 0 ) = 0.so that a(7)(0)( - 4) + b = 0. Then b = 0. Thus f ( x ) = a(x+7)(x - 0)( x -4) . We have f ( 7) = a ( 7 + 7)(7 - 0)(7 - 4) = a(14)(7)(3) = 294a. Therefore, we have 294a = -3. Therefore, a = -3/294 = - 1/98. Thus the required function is f ( x ) = (-1/98)(x+7)(x - 0)( x - 4)