Question

find the value of k in polynomial x²+8x+k, if -1 is a zero of the polynomial

Answer 1

The value of k is 7.

Step-by-step explanation:

1. Here polynomial is given

   $\mathbf{x^{2}+8x+k}$           ...1)

2. Polynomial equation will be written as

   $\mathbf{x^{2}+8x+k=0}$           ...2)

3. Here -1 is zero of  $\mathbf{x^{2}+8x+k}$. It means root of equation  $\mathbf{(x^{2}+8x+k=0)}$

4. It means

   x = -1   will satisfied the equation 2)

5. From equation 2)

   $\mathbf{x^{2}+8x+k=0}$          (putting value of x = -1)

 

   $\mathbf{(-1)^{2}+8(-1)+k=0}$

 

   $\mathbf{1-8+k=0}$        

 

   $\mathbf{-7+k=0}$

  So

  k=7

Answer 2

Given:

A quadratic polynomial x²+8x+k, where -1 is one of the zeroes of the given polynomial.

To Find:

The value of k in the given quadratic equation.

Solution:

The given problem can be solved using the concepts of polynomial equations.

1. The given polynomial equation is x²+8x+k, The equation is quadratic because the highest degree is 2.

2. The value of x when the value of y is 0 is said to be the zeroes/ roots of the polynomial equation. (OR) The number of points where the graph intersects or touches the x-axis is said to be the number of a polynomial equation.

3. Since -1 is one of the zeroes of the polynomial the value of y at x = -1 is zero.

=> 0 = (-1)² + 8(-1) + k,

=> 0 = 1 - 8 + k,

=> k -7 = 0,

=> k = 7.

Hence, The value of k is 7.

Therefore, the value of k is 7 and the complete polynomial equation is y = x²+8x+7.