Question

find the value of k. if one root is six times the other.​

Answer 1

Let roots be α and β

A/q

α = 6β  

now, if α and β are roots then equation will be (x -α)(x -β) =0

(x -α)(x -β) =0

⇒ x² - (α+β)x + αβ =0  

now putting α = 6β ,

⇒x² - (6β +β)x + 6β×β =0

⇒x² - 7βx +6β² =0  

now comparing with  kx² -14x +8 =0

7β =14/k

⇒β =2/k

⇒β² = 4/k²_______(1)

and 6β² =8/k

⇒β² =4/3k_______(2)

equating (1) and (2), we get,

4/k² = 4/3k

⇒k =3