Yuri thinks that is a root of the following function.q(x) = 6x3 + 19x2 – 15x – 28Explain to Yuri why cannot be a root.

Answer:

According to the Rational Root Theorem, a rational root must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. Since 3 is not a factor of 28 and 4 is not a factor of 6, 3/4 does not satisfy the theorem. Substituting 3/4 into the function gives -833/32, not 0, so it is not a root.