Question

if -4 is the zero of the polynomial p(x) = x^2+11x +k then find the value of k

Answer 1

P(x)=x²+11x+k

Since -4 is a zero of the polynomial P(x).

Put x= -4 in P(x).

=>P(-4)=(-4)²+11(-2)+k=0

=>16-22+k=0

=>k=6

Hope it is helpful.

Answer 2

Answer:

The value of k is 28

Step-by-step explanation:

Given that -4 is a zero of the polynomial x² + 11x + k.

To find:

• Value of k = ?

Solution:

f (x) = x² + 11x + k

Applying Factor theorem;

Since -4 is a zero of the polynomial, f(-4) would be equal to zero. For finding f(-4), put -4 in the place of x in the given f(x)

f (-4) = (-4)² + 11(-4) + k = 0

→ f (-4) = 16 - 44 + k = 0

→ f (-4) = -28 + k = 0

→ -28 + k = 0

→ k = 28

∴ The value of k is 28

KNOW MORE:

• If a polynomial f (x) is divided by (x - a), then the remainder is f(a). This is known as remainder theorem.
• If f (a) = 0, then (x - a) is a factor of f (x). This is factor theorem.