Question

If -4 is the zero of the polynomial p(x) = x² +11x + k, then find the value of k.

Answer 1

$\huge{ \mathfrak{we \: have}}$

p(x)=x² + 11x + K

To find the value of K

$\huge{ \mathfrak{given}} : \\ \sf{ - 4 \: is \: a \: zero \: of \: above \: polynomial}$

Here,

$\sf{p(x) = p( -4)}$

Thus,

p(-4)=(-4)²+11(-4)+K

=16-44+K

=K-28

By Remainder Theorm,

Any polynomial,p(x) is always equal to zero

Thus,

K-28=0

→K=28

Answer 2

Step-by-step explanation:

Hi,

(-4) is the one zero of the given polynomial x² +11x + k .

Therefore,

X = (-4)

Putting the value of x in x² + 11x + k .

P( x ) = 0

P(4) = (-4)² + 11 × -4 + k

=> 16 - 44 + k = 0

=> -28 + k = 0

=> k = 28

Hope it will help you :)