Question

If both x − 2 and \[x - \frac{1}{2}\] are factors of px² + 5x + r, then

Options

•  p = r

• p + r = 0

• 2p + r = 0

• p + 2r = 0

Answer 1

As (x - 2)and  (x - 1/2)are the factors of the polynomial `px^2 + 5x  + r`

i.e.,  f(2) = 0and  `f(1/2) = 0`

Now,

`f(2) = p(2)^2 + 5(2) + r = 0`

`4p + r = -10    ..... (1)`

And 

`f(1/2) = p(1/2)^2 + 5(1/2) + r = 0`

`p/4 + 5/2 + r = 0`

`p + 10 + 4x = 0`

`p+ 4x = -10         ........(2)`

From equation (1) and (2), we get

`4p + r = p + 4r`

       `3p = 3x`

          ` p = r`