examday

/TMUA

A polynomial $P(x)$ has degree $4$ and coefficient $1$ for $x^4$. Two of its real roots are $a$ and $b$, where $b-a=2$.

Consider the statements

• S: The tangents to $y=P(x)$ at $(a,0)$ and $(b,0)$ have the same gradient.
• T: $\displaystyle\int_a^b P(x)\,\mathrm{d}x=\frac{16}{15}$.

Which of the following correctly describes the relationship between S and T?