Question

What should be added to the polynomial $x^{2}-5x+4$, so that 3 is the zero of the resulting polynomial?
(a) 1
(b) 2
(c) 4
(d) 5

Answer 1

SOLUTION :  

The correct option is (b) : 2

A polynomial is exactly divisible by another polynomial, if remainder is zero. So , here find the remainder and add negative of remainder in f(x) , so that the resulting polynomial is divisible by g(x).

Given : f(x) = x² - 5x + 4

and one zero(x) = 3 ,  

So, x - 3 is a factor of f(x)  

Therefore, g(x) = x - 3

Now on Dividing f(x) by g(x) , we get the following division process.  

      x - 3 )x² - 5x + 4( x - 2

               x² - 3x  

               (-)   (+)  

          ----------------------

                 - 2x + 4

                 -2x + 6

                (+)  (-)  

         ------------------------

                         - 2

Here, Remainder is -2 . Now the polynomial  f(x) = x² - 5x + 4 will be exactly divisible by g(x) = x - 3 when Remainder is zero.  So to make the remainder 0 , 2 is to be added in f(x) .  

Hence, if we add 2 in  f(x) , then it will be divisible by g(x) =x - 3 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Heya....

Here's your answer.....

P (x) = x² - 5x + 4

P (3) = 3² - 5*3 + 4

P (3) = 9 - 15 + 4

P (3) = -2

Since, -2 is the remainder.

Therefore, 2 must be added to P(x) So that 3 will be a zero of the polynomial.

Thanks...!!!

XD

Sorry baby 'wink'