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, potential rational roots must be in the form p/q, where p is a factor of the constant term (-28) and q is a factor of the leading coefficient (6). Since 3 is not a factor of 28 and 4 is not a factor of 6, 3/4 cannot be a rational root. Additionally, substituting 3/4 into the function for x does not result in 0, and dividing the polynomial by (x - 3/4) would result in a non-zero remainder, confirming that 3/4 is not a root.