Question

FFind the value of k, for which one root of the quadratic equation kx2-14x+8=0 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