When we have two roots that are known, b and c, then we say that we can form a polynomial in the form: a(x - b)(x - c) = 0, where a is a real number.
This means that there are two roots, b and c, and the complexity of the leading coefficient is situated as a, an arbitrary real number.
Thus, we can say that a polynomial with roots 4/3 and 4 is actually:
[tex]a_1(x - \frac{4}{3})(x - 4) = 0[/tex]
[tex]a_1(3x - 4)(x - 4) = 0[/tex]
[tex]a_1(3x^{2} - 12x - 4x + 16) = 0[/tex]
[tex]a_1(3x^{2} - 16x + 16) = 0[/tex]
To find it in the form we want, let's distribute the a₁ into each term:
[tex]3a_1x^{2} - 16a_1x + 16a_1 = 0\text{, where }3a_1 = a\text{, } -16a_1 = b\text{, }16a_1 = c[/tex]
