Question

18. If a and B are the zeros of the polynomial f(x) = r- 5x + k such that a-B=1, find the value of k.​

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