Question

Find the value of p, for which one root of the quadratic equation px² – 14x + 8 = 0 is 6 times the other.

Answer 1

Let the first root be α, then the second root will be 6a

Sum of roots  =  `(-"b")/"a"`

`=> "a" + 6"a" = 14/"p"`

`=> 7"a" = 14/"p"`

`=> "a" = 2/"p"`

Product of roots = `"c"/"a"`

`=> "a"xx 6"a" = 8/"p"`

`=> 6"a"^2 = 8/"p"`

`=> 6(2/"p")^2 = 8/"p"`

`=>6xx4/"p"^2= 8/"p"`

`=>"p"=6xx4/8`

`=> "p" = 3`

Hence, the value of p is 3.