write down equations with integral coefficients having roots;(1/2,4).
(x-1/2)(x-4)=0
multiply it out.
To obtain equations with integral coefficients having roots (1/2,4), we can start by using the fact that if a polynomial has a root at a certain value, then the corresponding factor (x - root) is a factor of the polynomial.
In this case, the equation can be written as:
(x - 1/2)(x - 4) = 0.
To expand this equation, we can use the distributive property:
x(x - 4) - (1/2)(x - 4) = 0.
Multiplying both terms inside the parentheses:
x^2 - 4x - (1/2)x + 2 = 0.
Combining like terms:
x^2 - (9/2)x + 2 = 0.
This equation has integral coefficients (2, -9/2, and 1) and roots of (1/2, 4).