Answer:
The correct option is C.
Step-by-step explanation:
If a function f(x) is completely divisible by (x-a), it means (x-a) is a factor of f(x) and x=a is a root of that polynomial.
The given polynomial is
[tex]P(x)=2x^2+9x-5[/tex]
It is given that when David divide the above polynomial by (2x-1), then he get
[tex]Quotient=x+5[/tex]
[tex]Remainder=0[/tex]
Since the remainder is zero it means P(x) is completely divisible by (2x-1) or (2x-1) is a factor of P(x).
[tex]2x-1=0[/tex]
Add 1 on both the sides.
[tex]2x=1[/tex]
Divide both sides by 2.
[tex]x=\frac{1}{2}[/tex]
It means [tex]\frac{1}{2}[/tex] must be a root of the polynomial [tex]2x^2+9x-5[/tex].
Therefore, the correct option is C.
