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