Question

If the zeroes of the polynomial x^2 - 5x + k are the reciprocal of each other, then find the value of k.


plzz help guys....​

Answer 1

Answer:

The value of k is 1.

Step-by-step explanation:

Let the zeros of the polynomial be α and 1\α

We have= x^2 - 5x + k

To know :

Polynomial is an expression which consists of variables and coefficients in an expression

For example 7x+1, 3x+1/6

A polynomial involves only the operations must be addition, subtraction and multiplication

Polynomials occurs in many aspects of mathematics and science concepts.

Here In mathematics it is used a polynomial equations.

Product of zeros=c/a                                               [c=k a=1]

α x 1\α  =k/1 [ roots of the polynomial is given by alpha and beta]

k=1

Answer 2

Given, polynomial is x² - 5x + k

We have to find the value of k.

Read the question again.

“If the zeroes of the polynomial x² - 5x + k are the reciprocal of each other.”

Let one zero of the polynomial be x. (zeros are reciprocal of each other). So, the other zero is 1/x.

In the given polynomial, we have a = 1, b = -5 and c = k

We know that,

Sum of zeros = -b/a = -(-5)/1 = 5

If we do that, then we don't get the value of k.

So,

Product of zeros = c/a = k/1

By doing this we can find the value of k.

Now,

Product of zeros = c/a

→ x × 1/x = k/1

→ 1 = k/1

→ 1 = k

Therefore, the value of k is 1.