Question

In a polynomial x²-6x+k, find the value of 'k' such that (α+ß)² -2αß=40, where α and ß are the zeros of the given polynomial.

Answer 1

Answer:

Since a and b are the zeros of the polynomial f(x)=x  

2

−5x+k

The standard quadratic equation is px  

2

+qx+r=0  

Then Sum of roots = −  

p

q

​

 

and Product of roots =  

p

r

​

 

Therefore,

a+b=5 and ab=k

Now, a−b=1

(a−b)  

2

=1

(a+b)  

2

−4ab=1

25−4k=1

24=4k

k=6

Step-by-step explanation: