The roots of a polynomial are the zeros of the polynomial.
The functions have 1 and 6 as the roots are: (a) f(x) = (x – 1)(x – 6), (d) f(x) = 3(x – 1)(x – 6) and (e) 6(x – 1)(x – 6)
The roots are given as:
\(\mathbf{x = 1, x = 6}\)
Equate to 0
\(\mathbf{x - 1 = 0, x - 6 = 0}\)
Multiply the above expressions
\(\mathbf{(x - 1) \times (x -6) = 0 \times 0}\)
\(\mathbf{(x - 1) \times (x -6) = 0 }\)
Express as a function
\(\mathbf{f(x)= (x - 1) \times (x -6) }\)
\(\mathbf{f(x)= (x - 1)(x -6) }\)
As a general rule, we have:
\(\mathbf{f(x)=a (x - 1)(x -6) }\)
Where:
\(\mathbf{a
e 0}\)
\(\mathbf{f(x)=a (x - 1)(x -6) }\) represents all functions that have 1 and 6 as the roots.
So, options (a), (d) and (e) have 1 and 6 as the roots.
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