Question

Find the value of k if the quadratic equations is kx^2-14x+8=2

Answer 1

Hi dear

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