Question

If 3 is a zero of the polynomial x^2+2x+k,find the value of k and other zero

Answer 1

Given :- x = 3

• It is given that 3 is Zero of polynomial
x² + 2x + k. When we put value of x as 3 in the polynomial we get 0 as resultant.

x² + 2x + k = 0

( 3 )² + 2× 3 + k = 0

9 + 6 + k = 0

k = - 15

The required polynomial is
x² + 2x - 15 = 0

x² + 5x - 3x - 15 = 0

x ( x + 5 ) - 3 ( x + 5 ) = 0

( x - 3 ) ( x + 5 ) = 0

• ( x - 3 ) = 0
x = 3 ( given )

• ( x + 5 ) = 0
x = - 5

- 5 is the second Zero of polynomial.

Answer 2

Given , 3 is a zero of the polynomial, so it must satisfy the equation, i.e.
(3)^2 + 2(3) +k =0
or k = -15
so, we get the following polynomial :
x^2 + 2x -15 = 0
or, (x-3)(x+5) = 0
so the 2 zeros are 3, -5