Question

Find the number to be added to the polynomial x²-5x+4, so that 3 is the zero of the polynomial?

Answer 1

Let k be added to the polynomial.

Given Equation is p(x) = x^2 - 5x + (4 + k).

If 3 is the zero of the polynomial, then the equation will become p(3) = 0

p(3) = (3)^2 - 5(3) + (4 + k) = 0

9 - 15 + 4 + k = 0

- 6 + 4 + k = 0

-2 + k = 0

k = 2.


Therefore the number to be added to the polynomial is 2.