If the sum of the roots of the quadratic equation ky²-11y+(k-23) . . .

Question : If the sum of the roots of the quadratic equation ky²-11y+(k-23)=0 is 13/21 more than the products of the roots, then find the value of k.

Doubt by CBSE

Solution : 

ky²-11y+(k-23)=0

Here
a = k
b = -11

c = k-23

α+β = -b/a
α+β = -(-11)/k
α+β = 11/k — (1)

αβ = c/a

αβ = (k-23)/k — (2)

ATQ

α+β = (13/21) + αβ
α+β -αβ = 13/21

11/k-(k-23)/k = 13/21

(11-k+23)/k=13/21

(34-k)=13k/21
21(34-k)=13k
21×34-21k=13k
21×34=13k+21k
21×34=34k
21=k

Hence, k=21