Question

David performed the following mathematical operation .

Answer 1

Answer:

C:  x = 1/2

Step-by-step explanation:

Set the divisor, 2x - 1, equal to zero and solve for x:  2x = 1, so x = 1/2.  Statement C is true.

Answer 2

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

$P(x)=2x^2+9x-5$

It is given that when David divide the above polynomial by (2x-1), then he get

$Quotient=x+5$

$Remainder=0$

Since the remainder is zero it means P(x) is completely divisible by (2x-1) or (2x-1) is a factor of P(x).

$2x-1=0$

Add 1 on both the sides.

$2x=1$

Divide both sides by 2.

$x=\frac{1}{2}$

It means $\frac{1}{2}$ must be a root of the polynomial $2x^2+9x-5$.

Therefore, the correct option is C.