How do you write a polynomial with roots: −square root of 3, square root of 3, and 2?
A polynomial with three roots is a three-degree polynomial also known as a cubic polynomial.
Answer: The polynomial is written as y = x3 - 2x2 - 3x + 6.
Let's look into the solution step by step.
If a binomial has a root or zero as c, then the factor of the binomial is expressed as (x - c)
Since the roots are −√3, √3, 2, the polynomial can be expressed as:
⇒ y = (x - (-√3))(x - √3)(x - 2)
⇒ y = (x + √3)(x - √3)(x - 2)
⇒ y = (x2 - 3)(x - 2)
⇒ y = (x3 - 2x2 - 3x + 6)
Thus, the polynomial is written as y = x3 - 2x2 - 3x + 6.