Answer:
p(x) = x² +30x -375
Step-by-step explanation:
When a quadratic has real rational coefficients, any irrational or complex roots come in conjugate pairs.
Factored form
A root of p means (x -p) is a factor of the polynomial. Here, we have roots of -15+10√6 and -15-10√6, so the factored form can be written ...
p(x) = (x -(-15 +10√6))(x -(-15 -10√6))
Using the factoring of the difference of squares, we can write this as ...
p(x) = (x +15)² -(10√6)²
Standard form
Expanding the factored form, we can write the polynomial as ...
p(x) = x² +30x +225 -600
p(x) = x² +30x -375
