Question

if alpha of the polynomial x square - 5 x + K such that Alpha minus b = 1 then find the k​

Answer 1

Answer:

Correct question:

If alpha and beta are the zeros of polynomial x^2 - 5x + k such that

alpha - beta = 1 , then find the value of k.

Note:

Considering alpha as A and beta as B.

Here,

The given quadratic polynomial is:

x^2 - 5x + k.

We know that ,

The sum of zeros of a quadratic polynomial is given by (-b/a).

Thus,

A + B = -(-5)/1 = 5 -------(1)

Also,

The product of zeros of a quadratic polynomial is given by (c/a).

A•B = k/1 = k -------(2)

Also,

It is given that;

A - B = 1 ---------(3)

Note:

(A+B)^2 = (A - B)^2 + 4•A•B

Now,

Putting the appropriate values of (A+B) , (A-B) and A•B in above formula,

We get;

=> (A+B)^2 = (A - B)^2 + 4•A•B

=> (5)^2 = (1)^2 + 4•k

=> 25 = 1 + 4•k

=> 4•k = 25 - 1

=> 4•k = 24

=> k = 24/4

=> k = 6

Hence, the required value of k is 6.