Question

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

Answer 1

Given, quadratic equation is ky² – 11y + (k – 23) = 0

Let the roots of the above quadratic equation be α and β.

Now, Sum of roots, α + β = `(-(-11))/k = 11/k`  ...(i)

and Product of roots, αβ = `(k - 23)/k`  ...(ii)

According to the question,

α + β = αβ + `13/21`

∴ `11/k = (k - 23)/k + 13/21`  ...[From equations (i) and (ii)]

⇒ `11/k - ((k - 23))/k = 13/21`

⇒ `(11 - k + 23)/k = 13/21`

⇒ 21(34 – k) = 13k

⇒ 714 – 21k = 13k

⇒ 714 = 13k + 21k

⇒ 34k = 714

⇒ k = `714/34`

⇒ k = 21