Question

if 2 is a zero of the polynomial x^2+2x+k find k also find the other zero​

Answer 1

Answer :-

If 2 is a zero of polynomial, then p(2) = 0

Substituting the value x = 2 in polynomial :-

→ $\sf x^2 + 2x + k = 0$

→ $\sf 2^2 + 2(2) + k = 0$

→ $\sf 4 + 4 + k = 0$

→ $\sf k + 8 = 0$

→ $\boxed{\sf k = -8 }$

Also, if 2 is zero of polynomial then (x - 2) is a factor of polynomial.

So, by dividing ( x - 2 ) from x² + 2x - 8 we can get other zero -

$\sf\Large\qquad\quad \:\:\:x + 4\\ \begin{array}{cc} \cline{2 - 2}\sf x - 2)&\sf \ x^2 + 2x - 8\\&\sf - x^2 + 2x \downarrow\\ \cline{2-2}& \sf \ \ \ \ 4x - 8\\ &\sf \ - 4x + 8 \\ \cline{2-2} & \sf \ \000 \\ \cline{2-2} \end{array}$

Other factor = x + 4

So, other zero, x + 4 = 0

x = - 4

Other zero = -4