Question

David performed the following mathematical operation .

Answer 1

The correct option is C.

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=(1)/(2)`

It means
`(1)/(2)` must be a root of the polynomial
`2x^2+9x-5`.

Therefore, the correct option is C.

Answer 2

C: x = 1/2

Explanation:

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