========================================================== The given graph have four zeros at x = -3 , 0 , 2 , 7 ========================================================== f(x) = x³ + x² -6x The function f(x) is polynomial has degree = 3 so, it has only 3 zeros ========================================================== g(x) = (x²+x-6)(x²-7x) ⇒ By factoring ⇒ By factoring ∴ g(x) = x(x-7)(x+3)(x-2) ∴ g(x) has zeros at x = -3 , 0 , 2 , 7 ========================================================== h(x) = x(x-7)(x+3)(x-2) h(x) has zeros at x = -3 , 0 , 2 , 7 ========================================================== m(x) = (x³-4x²-21x)(x-2) ⇒ By factoring ∴ m(x) = x(x-7)(x+3)(x-2) ∴ m(x) has zeros at x = -3 , 0 , 2 , 7 ========================================================== n(x) = x²-9x+14 The function f(x) is polynomial has degree = 3 so, it has only 3 zeros ========================================================== p(x) = x(x+2)(x-3)(x+7) ∴ p(x) has zeros at x = 3 , 0 , -2 , -7 ========================================================== By comparing zeros of the given graph to zeros of the functions The result will be: <span>The functions that have the same zeros as the graph</span> are g(x) , h(x) and m(x)
