Question

what should be subtracted from the polynomial x2-4x-6 so that 5 is a zero of the polynomial

Answer 1

Answer:

Given :

   p(x) = x² - 4x - 6

   5 should be zero of the polynomial.

⇒therefore,

           p(x) = x² - 4x - 6

           p(5)  = (5)² - 4 * (5) - 6

                  = 25 - 20 - 6

                  = 5 - 6

                  =  -1

∴ -1 should be subtracted.

Verification⇒

             p(x) = x² - 4x - 6 -(-1)

                    = x² - 4x -6 + 1

                    = x² - 4x -5

  ∴ p(5) = [5² - (4 * 5)] -5

             = [25 - 20]  - 5

             = 5 - 5

              = 0

             Hence verified    

                   

             

Step-by-step explanation:

Answer 2

Answer:

Required number is -1

Step-by-step explanation:

Given polynomial is:

p(x) = $x^{2} - 4x - 6$

Let the number which is to be subtracted so that 5 will be zero of the given polynomial be y.

Then,

$5^{2} - 4*5 - 6 -y = 0\\25 - 20 - 6 - y = 0 \\25 - 26 -y = 0\\-1 - y = 0 \\y = -1$

Thus, required number is -1.