Answer:
Since [tex]q(\frac{3}{4}) \neq 0[/tex], 3/4 cannot be a root of q(x).
Step-by-step explanation:
Root of a function:
If [tex]x^{\ast}[/tex] is a root of a function f(x), we have that [tex]f(x^{\ast}) = 0[/tex].
In this question.
We have to find [tex]q(\frac{3}{4})[/tex]. So
[tex]q(\frac{3}{4}) = 6(\frac{3}{4})^3 + 19(\frac{3}{4})^2 - 15(\frac{3}{4}) - 28[/tex]
[tex]q(\frac{3}{4}) = \frac{162}{64} + \frac{171}{16} - \frac{45}{4} - 28[/tex]
[tex]q(\frac{3}{4}) = \frac{162}{64} + \frac{684}{64} - \frac{720}{64} - \frac{1792}{64}[/tex]
[tex]q(\frac{3}{4}) \neq 0[/tex]
Since [tex]q(\frac{3}{4}) \neq 0[/tex], 3/4 cannot be a root of q(x).
