Question

Which function has real zeros at x = 3 and x = 7?

A- f(x) = x^2 + 4x – 21
B- f(x) = x^2 – 4x – 21
C- f(x) = x^2 – 10x + 21
D- f(x) = x^2 – 10x – 21

Answer 1

f(x) = (x - 3)(x - 7)
expanding the brackets gives:
f(x) = x^2 - 10x + 21

Answer 2

f(x) = x² - 10x + 21

Explanation:

Functions that has real zeros at x = 3 and x = 7 are the function that produces the roots of 3 and 7 after factorising.

Having two roots as given;

x = 3 and

x = 7

If x=3 then x -3 = 0... 1

Similarly;

If x = 7 then x-7 = 0... 2

Multiplying the zero functions in equation 1 and 2 together we have;

f(x) = (x-3)(x-7)

f(x) = x²-7x-3x+21

f(x) = x² - 10x + 21 = 0

The polynomial or quadratic function above gives the required function.