Question

Write a polynomial of at least degree with roots 6 and 7

Answer 1

f(x) = (x - 6)(x - 7)

Now, you can expand this expression to obtain the polynomial in standard form:

f(x) = (x - 6)(x - 7)

f(x) = x(x - 7) - 6(x - 7)

Now, distribute and simplify:

f(x) = x(x) - x(7) - 6(x) + 6(7)

f(x) = x^2 - 7x - 6x + 42

Combine like terms:

f(x) = x^2 - 13x + 42

So, the polynomial with roots 6 and 7 is f(x) = x^2 - 13x + 42. This is a polynomial of degree 2 (quadratic) with the given roots.